Expand the Trigonometric Expression cot(-x)cos(-x)+sin(-x)

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Trigonometry

$\cot (- x) \cos (- x) + \sin (- x)$

Simplify each term.

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Since $\cot (- x)$ is an odd function, rewrite $\cot (- x)$ as $- \cot (x)$ .

$- \cot (x) \cos (- x) + \sin (- x)$

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

$- \frac{\cos (x)}{\sin (x)} \cos (- x) + \sin (- x)$

Since $\cos (- x)$ is an even function, rewrite $\cos (- x)$ as $\cos (x)$ .

$- \frac{\cos (x)}{\sin (x)} \cos (x) + \sin (- x)$

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

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

$- \frac{\cos (x) \cos (x)}{\sin (x)} + \sin (- x)$

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

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

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

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

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

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

Add $1$ and $1$ .

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

Since $\sin (- x)$ is an odd function, rewrite $\sin (- x)$ as $- \sin (x)$ .

$- \frac{\cos^{2} (x)}{\sin (x)} - \sin (x)$

Simplify each term.

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

$- \frac{\cos (x) \cos (x)}{\sin (x)} - \sin (x)$

Separate fractions.

$- (\frac{\cos (x)}{1} \cdot \frac{\cos (x)}{\sin (x)}) - \sin (x)$

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

$- (\frac{\cos (x)}{1} \cot (x)) - \sin (x)$

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

$- \cos (x) \cot (x) - \sin (x)$

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Name

Name	one billion three hundred three million four hundred seventy-six thousand nine hundred forty

Interesting facts

1303476940 has 32 divisors, whose sum is 3520493280
The reverse of 1303476940 is 0496743031
Previous prime number is 3943

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 37
Digital Root 1

Name

Name	one billion four hundred ninety-seven million eight hundred eighty-seven thousand six hundred twenty

Interesting facts

1497887620 has 32 divisors, whose sum is 4046112000
The reverse of 1497887620 is 0267887941
Previous prime number is 2399

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 52
Digital Root 7

Name

Name	three hundred thirty-eight million five hundred ninety-one thousand five hundred forty-four

Interesting facts

338591544 has 32 divisors, whose sum is 1523662056
The reverse of 338591544 is 445195833
Previous prime number is 3

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 42
Digital Root 6

Determine if True cos((3pi)/8)=cos(1/2)cos((3pi)/2)

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