Solve for ? tan(x)+cot(x)=csc(x)sec(x)

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Trigonometry

$\tan (x) + \cot (x) = \csc (x) \sec (x)$

Since $\sec (x)$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$\csc (x) \sec (x) = \tan (x) + \cot (x)$

Divide each term by $\csc (x)$ and simplify.

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Divide each term in $\csc (x) \sec (x) = \tan (x) + \cot (x)$ by $\csc (x)$ .

$\frac{\csc (x) \sec (x)}{\csc (x)} = \frac{\tan (x)}{\csc (x)} + \frac{\cot (x)}{\csc (x)}$

Reduce the expression by cancelling the common factors.

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Cancel the common factor.

$\frac{\csc (x) \sec (x)}{\csc (x)} = \frac{\tan (x)}{\csc (x)} + \frac{\cot (x)}{\csc (x)}$

Divide $\sec (x)$ by $1$ .

$\sec (x) = \frac{\tan (x)}{\csc (x)} + \frac{\cot (x)}{\csc (x)}$

Simplify each term.

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Rewrite $\csc (x)$ in terms of sines and cosines.

$\sec (x) = \frac{\tan (x)}{\frac{1}{\sin (x)}} + \frac{\cot (x)}{\csc (x)}$

Rewrite $\tan (x)$ in terms of sines and cosines.

$\sec (x) = \frac{\frac{\sin (x)}{\cos (x)}}{\frac{1}{\sin (x)}} + \frac{\cot (x)}{\csc (x)}$

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\sin (x)}$ .

$\sec (x) = \frac{\sin (x)}{\cos (x)} \cdot \sin (x) + \frac{\cot (x)}{\csc (x)}$

Write $\sin (x)$ as a fraction with denominator $1$ .

$\sec (x) = \frac{\sin (x)}{\cos (x)} \cdot \frac{\sin (x)}{1} + \frac{\cot (x)}{\csc (x)}$

Simplify.

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Divide $\sin (x)$ by $1$ .

$\sec (x) = \frac{\sin (x)}{\cos (x)} \cdot \sin (x) + \frac{\cot (x)}{\csc (x)}$

Convert from $\frac{\sin (x)}{\cos (x)}$ to $\tan (x)$ .

$\sec (x) = \tan (x) \sin (x) + \frac{\cot (x)}{\csc (x)}$

Rewrite $\csc (x)$ in terms of sines and cosines.

$\sec (x) = \tan (x) \sin (x) + \frac{\cot (x)}{\frac{1}{\sin (x)}}$

Rewrite $\cot (x)$ in terms of sines and cosines.

$\sec (x) = \tan (x) \sin (x) + \frac{\frac{\cos (x)}{\sin (x)}}{\frac{1}{\sin (x)}}$

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\sin (x)}$ .

$\sec (x) = \tan (x) \sin (x) + \frac{\cos (x)}{\sin (x)} \cdot \sin (x)$

Write $\sin (x)$ as a fraction with denominator $1$ .

$\sec (x) = \tan (x) \sin (x) + \frac{\cos (x)}{\sin (x)} \cdot \frac{\sin (x)}{1}$

Cancel the common factor of $\sin (x)$ .

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Factor out the greatest common factor $\sin (x)$ .

$\sec (x) = \tan (x) \sin (x) + \frac{\cos (x)}{\sin (x) \cdot 1} \cdot \frac{\sin (x) \cdot 1}{1}$

Cancel the common factor.

$\sec (x) = \tan (x) \sin (x) + \frac{\cos (x)}{\sin (x) \cdot 1} \cdot \frac{\sin (x) \cdot 1}{1}$

Rewrite the expression.

$\sec (x) = \tan (x) \sin (x) + \frac{\cos (x)}{1} \cdot \frac{1}{1}$

Simplify.

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Divide $\cos (x)$ by $1$ .

$\sec (x) = \tan (x) \sin (x) + \cos (x) (\frac{1}{1})$

Divide $1$ by $1$ .

$\sec (x) = \tan (x) \sin (x) + \cos (x) \cdot 1$

Multiply $\cos (x)$ by $1$ .

$\sec (x) = \tan (x) \sin (x) + \cos (x)$

Simplify $\tan (x) \sin (x) + \cos (x)$ .

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Simplify each term.

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Rewrite $\tan (x)$ in terms of sines and cosines.

$\sec (x) = \frac{\sin (x)}{\cos (x)} \cdot \sin (x) + \cos (x)$

Simplify $\frac{\sin (x)}{\cos (x)} \sin (x)$ .

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Write $\sin (x)$ as a fraction with denominator $1$ .

$\sec (x) = \frac{\sin (x)}{\cos (x)} \cdot \frac{\sin (x)}{1} + \cos (x)$

Multiply $\frac{\sin (x)}{\cos (x)}$ and $\frac{\sin (x)}{1}$ .

$\sec (x) = \frac{\sin (x) \sin (x)}{\cos (x)} + \cos (x)$

Raise $\sin (x)$ to the power of $1$ .

$\sec (x) = \frac{\sin (x) \sin (x)}{\cos (x)} + \cos (x)$

Raise $\sin (x)$ to the power of $1$ .

$\sec (x) = \frac{\sin (x) \sin (x)}{\cos (x)} + \cos (x)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sec (x) = \frac{{\sin (x)}^{1 + 1}}{\cos (x)} + \cos (x)$

Add $1$ and $1$ .

$\sec (x) = \frac{\sin^{2} (x)}{\cos (x)} + \cos (x)$

Simplify each term.

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Factor $\sin (x)$ out of $\sin^{2} (x)$ .

$\sec (x) = \frac{\sin (x) \sin (x)}{\cos (x)} + \cos (x)$

Separate fractions.

$\sec (x) = \frac{\sin (x)}{1} \cdot \frac{\sin (x)}{\cos (x)} + \cos (x)$

Convert from $\frac{\sin (x)}{\cos (x)}$ to $\tan (x)$ .

$\sec (x) = \frac{\sin (x)}{1} \cdot \tan (x) + \cos (x)$

Divide $\sin (x)$ by $1$ .

$\sec (x) = \sin (x) \tan (x) + \cos (x)$

Divide each term in the equation by $\cos (x)$ .

$\frac{\sec (x)}{\cos (x)} = \frac{\sin (x) \tan (x) + \cos (x)}{\cos (x)}$

Rewrite $\sec (x)$ in terms of sines and cosines.

$\frac{\frac{1}{\cos (x)}}{\cos (x)} = \frac{\sin (x) \tan (x) + \cos (x)}{\cos (x)}$

Rewrite $\frac{\frac{1}{\cos (x)}}{\cos (x)}$ as a product.

$\frac{1}{\cos (x)} \cdot \frac{1}{\cos (x)} = \frac{\sin (x) \tan (x) + \cos (x)}{\cos (x)}$

Multiply $\frac{1}{\cos (x)}$ and $\frac{1}{\cos (x)}$ .

$\frac{1}{\cos (x) \cos (x)} = \frac{\sin (x) \tan (x) + \cos (x)}{\cos (x)}$

Simplify the denominator.

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Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{{\cos (x)}^{1 + 1}} = \frac{\sin (x) \tan (x) + \cos (x)}{\cos (x)}$

Add $1$ and $1$ .

$\frac{1}{\cos^{2} (x)} = \frac{\sin (x) \tan (x) + \cos (x)}{\cos (x)}$

Simplify with factoring out.

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Rewrite $1$ as $1^{2}$ .

$\frac{1^{2}}{\cos^{2} (x)} = \frac{\sin (x) \tan (x) + \cos (x)}{\cos (x)}$

Rewrite $\frac{1^{2}}{\cos^{2} (x)}$ as ${(\frac{1}{\cos (x)})}^{2}$ .

${(\frac{1}{\cos (x)})}^{2} = \frac{\sin (x) \tan (x) + \cos (x)}{\cos (x)}$

Convert from $\frac{1}{\cos (x)}$ to $\sec (x)$ .

$\sec^{2} (x) = \frac{\sin (x) \tan (x) + \cos (x)}{\cos (x)}$

Replace $\cos (x)$ with an equivalent expression in the numerator.

$\sec^{2} (x) = (\sin (x) \tan (x) + \cos (x)) \cdot \sec (x)$

Remove parentheses.

$\sec^{2} (x) = (\sin (x) \tan (x) + \cos (x)) \cdot \sec (x)$

Multiply $\sin (x) \tan (x) + \cos (x)$ by $\sec (x)$ .

$\sec^{2} (x) = (\sin (x) \tan (x) + \cos (x)) \sec (x)$

Apply the distributive property.

$\sec^{2} (x) = \sin (x) \tan (x) \sec (x) + \cos (x) \sec (x)$

Rewrite $\tan (x)$ in terms of sines and cosines.

$\sec^{2} (x) = \sin (x) (\frac{\sin (x)}{\cos (x)}) \cdot \sec (x) + \cos (x) \sec (x)$

Simplify $\sin (x) \frac{\sin (x)}{\cos (x)}$ .

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Write $\sin (x)$ as a fraction with denominator $1$ .

$\sec^{2} (x) = \frac{\sin (x)}{1} \cdot \frac{\sin (x)}{\cos (x)} \cdot \sec (x) + \cos (x) \sec (x)$

Multiply $\frac{\sin (x)}{1}$ and $\frac{\sin (x)}{\cos (x)}$ .

$\sec^{2} (x) = \frac{\sin (x) \sin (x)}{\cos (x)} \cdot \sec (x) + \cos (x) \sec (x)$

Raise $\sin (x)$ to the power of $1$ .

$\sec^{2} (x) = \frac{\sin (x) \sin (x)}{\cos (x)} \cdot \sec (x) + \cos (x) \sec (x)$

Raise $\sin (x)$ to the power of $1$ .

$\sec^{2} (x) = \frac{\sin (x) \sin (x)}{\cos (x)} \cdot \sec (x) + \cos (x) \sec (x)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sec^{2} (x) = \frac{{\sin (x)}^{1 + 1}}{\cos (x)} \cdot \sec (x) + \cos (x) \sec (x)$

Add $1$ and $1$ .

$\sec^{2} (x) = \frac{\sin^{2} (x)}{\cos (x)} \cdot \sec (x) + \cos (x) \sec (x)$

Rewrite $\sec (x)$ in terms of sines and cosines.

$\sec^{2} (x) = \frac{\sin^{2} (x)}{\cos (x)} \cdot \frac{1}{\cos (x)} + \cos (x) \sec (x)$

Simplify $\frac{\sin^{2} (x)}{\cos (x)} \cdot \frac{1}{\cos (x)}$ .

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Multiply $\frac{\sin^{2} (x)}{\cos (x)}$ and $\frac{1}{\cos (x)}$ .

$\sec^{2} (x) = \frac{\sin^{2} (x)}{\cos (x) \cos (x)} + \cos (x) \sec (x)$

Raise $\cos (x)$ to the power of $1$ .

$\sec^{2} (x) = \frac{\sin^{2} (x)}{\cos (x) \cos (x)} + \cos (x) \sec (x)$

Raise $\cos (x)$ to the power of $1$ .

$\sec^{2} (x) = \frac{\sin^{2} (x)}{\cos (x) \cos (x)} + \cos (x) \sec (x)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sec^{2} (x) = \frac{\sin^{2} (x)}{{\cos (x)}^{1 + 1}} + \cos (x) \sec (x)$

Add $1$ and $1$ .

$\sec^{2} (x) = \frac{\sin^{2} (x)}{\cos^{2} (x)} + \cos (x) \sec (x)$

Convert from $\frac{\sin^{2} (x)}{\cos^{2} (x)}$ to $\tan^{2} (x)$ .

$\sec^{2} (x) = \tan^{2} (x) + \cos (x) \sec (x)$

Rewrite in terms of sines and cosines, then cancel the common factors.

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Reorder $\cos (x)$ and $\sec (x)$ .

$\sec^{2} (x) = \tan^{2} (x) + \sec (x) \cos (x)$

Rewrite $\cos (x) \sec (x)$ in terms of sines and cosines.

$\sec^{2} (x) = \tan^{2} (x) + \frac{1}{\cos (x)} \cdot \cos (x)$

Cancel the common factors.

$\sec^{2} (x) = \tan^{2} (x) + 1$

Replace $1 + t a n^{2} (x)$ with $s e c^{2} (x)$ using the identity $s e c^{2} (x) = 1 + t a n^{2} (x)$ .

$\sec^{2} (x) = \sec^{2} (x)$

This is the proper way of writing a trigonometric expression raised to an exponent.

$\sec^{2} (x) = 1 \sec^{2} (x)$

Multiply $\sec^{2} (x)$ by $1$ .

$\sec^{2} (x) = \sec^{2} (x)$

This is the proper way of writing a trigonometric expression raised to an exponent.

$\sec^{2} (x) = 1 \sec^{2} (x)$

Multiply $\sec^{2} (x)$ by $1$ .

$\sec^{2} (x) = \sec^{2} (x)$

This is the proper way of writing a trigonometric expression raised to an exponent.

$\sec^{2} (x) = 1 \sec^{2} (x)$

Multiply $\sec^{2} (x)$ by $1$ .

$\sec^{2} (x) = \sec^{2} (x)$

For the two functions to be equal, the arguments of each must be equal.

$x = x$

Move all terms containing $x$ to the left side of the equation.

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Subtract $x$ from both sides of the equation.

$x - x = 0$

Subtract $x$ from $x$ .

$0 = 0$

Since $0 = 0$ , the equation will always be true for any value of $x$ .

All real numbers

Do you know how to Solve for ? tan(x)+cot(x)=csc(x)sec(x)? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name

Name	one billion three hundred forty-five million eight hundred eighty-two thousand eight hundred sixty-five

Interesting facts

1345882865 has 16 divisors, whose sum is 1629783936
The reverse of 1345882865 is 5682885431
Previous prime number is 1031

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 50
Digital Root 5

Name

Name	four hundred forty-seven million two hundred sixty-one thousand two hundred sixty-six

Interesting facts

447261266 has 8 divisors, whose sum is 700061184
The reverse of 447261266 is 662162744
Previous prime number is 23

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 38
Digital Root 2

Name

Name	one billion eight hundred ninety-three million nine hundred eighty-six thousand eight hundred fifty-five

Interesting facts

1893986855 has 4 divisors, whose sum is 2272784232
The reverse of 1893986855 is 5586893981
Previous prime number is 5

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 62
Digital Root 8

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