Verify that each equation is an identity.
sin² α + tan² ...

Question

Verify that each equation is an identity.

sin² α + tan² α + cos² α = sec² α

Accepted Answer

Hello. Today we're going to be verifying whether the given equation is an identity or not. In order to show that the equation is an identity, we want to prove that the left hand side of the equation is equal to the right hand side of the equation. If we take a look at what is given to us, we are given seek and squared of theta plus co tangent squared of theta minus tangent squared of theta is equal to coin squared of theta. Now, in order to approach this problem, we're going to rewrite the equation slightly. Let's go ahead and group up the C and square the term and tangent squared, the term together we can rewrite the equation as second squared of theta minus tangent squared of theta plus co tangent squared of the is equal to co seek and squared of the. Now you may be wondering why we rewrote the equation like this. Well, keep in mind that we have a Pythagorean identity that relates sin squared and canyon squared together that Pythagorean identity is given to us as tangent squared of theta plus one is equal to seek and squared of theta. If we were to subtract tangent squared to both sides of this identity. We can rewrite the identity as one is equal to seek and squared of theta minus tangent squared of theta. The right hand side of this identity matches the grouped up terms that we rewrote. So what this means is that we can replace sequin squared data minus tangent squared data with one doing so will allow us to rewrite the equation as one plus cotangent squared of theta is equal to coin squared theta. Now there's one more thing that we can do in order to further simplify the left hand side, recall that the Pythagorean identity for cos and squared of theta is equal to one plus cotangent squared. Theta. What this means is that we can use this identity to rewrite the left hand side of the equation as co seek and squared of theta. And that is going to be equal to co seek and squared of the which is a true statement. So this verifies that the given equation is an identity. Therefore, the answer to this problem is going to be a. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

Struggling with Trigonometry?

Verify that each equation is an identity.
sin² α + tan² α + cos² α = sec² α

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Struggling with Trigonometry?

Verify that each equation is an identity.sin² α + tan² α + cos² α = sec² α

Watch next

Introduction to Trigonometric Identities practice set

Verify that each equation is an identity.
sin² α + tan² α + cos² α = sec² α