Verify the Identity sin(theta)^2sec(theta)^2=sec(theta)^2-1

Solve Math

Trigonometry

$\sin^{2} (θ) \sec^{2} (θ) = \sec^{2} (θ) - 1$

Start on the left side.

$\sin^{2} (θ) \sec^{2} (θ)$

Apply Pythagorean identity in reverse.

$(1 - \cos^{2} (θ)) \sec^{2} (θ)$

Convert to sines and cosines.

Tap for more steps...

Apply the reciprocal identity to $\sec (θ)$ .

$(1 - \cos^{2} (θ)) {(\frac{1}{\cos (θ)})}^{2}$

Apply the product rule to $\frac{1}{\cos (θ)}$ .

$(1 - \cos^{2} (θ)) \frac{1^{2}}{\cos^{2} (θ)}$

Simplify.

Tap for more steps...

One to any power is one.

$(1 - {\cos (θ)}^{2}) \frac{1}{{\cos (θ)}^{2}}$

Apply the distributive property.

$1 \frac{1}{{\cos (θ)}^{2}} - {\cos (θ)}^{2} \frac{1}{{\cos (θ)}^{2}}$

Multiply $\frac{1}{{\cos (θ)}^{2}}$ by $1$ .

$\frac{1}{{\cos (θ)}^{2}} - {\cos (θ)}^{2} \frac{1}{{\cos (θ)}^{2}}$

Cancel the common factor of ${\cos (θ)}^{2}$ .

$\frac{1}{\cos^{2} (θ)} - 1$

Reorder terms.

$- 1 + \frac{1}{\cos^{2} (θ)}$

Rewrite $- 1 + \frac{1}{\cos^{2} (θ)}$ as $\sec^{2} (θ) - 1$ .

$\sec^{2} (θ) - 1$

Because the two sides have been shown to be equivalent, the equation is an identity.

$\sin^{2} (θ) \sec^{2} (θ) = \sec^{2} (θ) - 1$ is an identity

Do you know how to Verify the Identity sin(theta)^2sec(theta)^2=sec(theta)^2-1? 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 two hundred fifty-five million nine hundred thirty-two thousand eight hundred twenty-five

Interesting facts

1255932825 has 32 divisors, whose sum is 1605132288
The reverse of 1255932825 is 5282395521
Previous prime number is 7

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 42
Digital Root 6

Name

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

Interesting facts

1254956373 has 16 divisors, whose sum is 1546948800
The reverse of 1254956373 is 3736594521
Previous prime number is 59

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 45
Digital Root 9

Name

Name	eight hundred forty-nine million three hundred seventy-seven thousand nine hundred one

Interesting facts

849377901 has 16 divisors, whose sum is 1148130560
The reverse of 849377901 is 109773948
Previous prime number is 1321

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 48
Digital Root 3

Verify the Identity (cot(B)^2-cos(B)^2)/(csc(B)^2-1)=cos(B)^2

Graph y=-2sin(3(x-pi/8))

Simplify cot(25)

Find the Reference Angle (11pi)/7

Find the Exact Value csc(405)