In Exercises 1–60, verify each identity.

cos² θ (1 + tan² θ) = 1

Question

In Exercises 1–60, verify each identity.

cos² θ (1 + tan² θ) = 1

Accepted Answer

Hello, everybody. I hope we're doing right today. So we're going to be talking about this question that states determine whether the given identity is true or false where our identity is open parentheses, one minus cosine squared M closed parentheses, multiplied by open parentheses cos squared M closed and that will be equal to one. Now, the answer is provided we only have two A being true and B being false. Now, for a question like this first, I'm going to rewrite our equation. And what we wanna do here is basically, usually we tackle the left hand side of the equation and then the right hand side and just basically prove they're both equal to each other. Now, since we all have this equal to one, we just have to prove that the left hand side of our equation is equal to one. So I write our equation first just so I have a bit more room to work with. So first things first, let's recall. So I can recall that one minus cosine squared M is equal to sine squared M. And this is thanks to a Python identity. And I can also recall that co C squared M is equal to one divided by sine squared M. And now with those recalls, I can rewrite and I'll rewrite my equation and it'll be open parentheses. Sine squared M closed parentheses multiplied by one divided by sine squared M closed parentheses. And that'll be equal to one. Now, if we distribute our two multiplications, we'll have sine squared M divided by sine squared M and that'll be equal to one. And when you have a fraction with the same number in the numerator and the denominator, we have a fraction of one. So we're left with one equals one which checks out. And that means that our identity is true. So I hope that was helpful. And until next time.

In Exercises 1–60, verify each identity. cos² θ (1 + tan² θ) = 1

Key Concepts

Pythagorean Identity

Tangent and Secant Relationship

Trigonometric Identities

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