Verify that each equation is an identity (Hint: cos 2x = cos(x...

Question

Verify that each equation is an identity (Hint: cos 2x = cos(x + x).)

cos 2x = (cot² x - 1)/(cot² x + 1)

Accepted Answer

Hello, everyone. We are asked if the given equation is an identity, we are given the cosine of two X equals one minus the cosine squared of X divided by the sine squared of X. Our answer choices are a yes B no. To prove this is an identity, we need to make the left hand side match the right hand side. Looking at the right hand side, I think that's where I'm going to start. So we are given one minus the cosine squared of X divided by the sine squared of X. And I recall we have a Pythagorean identity that states that the sine squared of X plus the cosine squared of X equals one. So if I were to rearrange that by subtracting the cosine squared of X from both sides, I would get that the sine squared of X equals one minus cosine squared X. This means on my right hand side, I can substitute the sine squared of X in for my numerator. And when I do, I get the sine squared of X divided by the sine squared of X A value divided by itself always equals one. So the right hand side of our equation here equals one. Looking at the left hand side cosine of two X, I do not believe there's any way to make this equal one. Even if I work with the identities we're given of what the cosine of two X could equal, it doesn't equal one. So the answer here is answer choice B no, this is not an identity. Have a nice day.

Struggling with Trigonometry?

Verify that each equation is an identity (Hint: cos 2x = cos(x + x).)
cos 2x = (cot² x - 1)/(cot² x + 1)

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Struggling with Trigonometry?

Verify that each equation is an identity (Hint: cos 2x = cos(x + x).)cos 2x = (cot² x - 1)/(cot² x + 1)

Watch next

Sum and Difference Identities practice set

Verify that each equation is an identity (Hint: cos 2x = cos(x + x).)
cos 2x = (cot² x - 1)/(cot² x + 1)