Simplify each expression.
±√[(1 - cos 5A)/(1 + ...

Question

Simplify each expression.

±√[(1 - cos 5A)/(1 + cos 5A)]

Accepted Answer

Welcome back. I am so glad you're here. We're asked to use a trigonometric identity to simplify the expression. Our given expression is plus or minus the square root of. And we have a radical with a fraction inside of it. In the numerator of our fraction, we have one minus the cosine of 11 B that's divided by still inside the radical. In the denominator, we have one plus the cosine of 11 B. Our answer choices are answer choice A, the sine of 11 B divided by four. Answer choice B, the cotangent of 11 B divided by two. Answer choice C, the cosine of 22 B and answer choice D, the tangent of 11 B divided by two. All right. So we're calling from previous lessons and from those charts in the textbook with different trigonometric identities. This one looks a lot like a half angle identity, specifically one where we have plus or minus the square rut of. And then inside of the radical, we have a fraction in the numerator. We have one minus the cosine of A and that's divided by one plus the cosine of A that is all equal to the tangent of A divided by two, our half angle identity. And so comparing our given expression with our half angle identity, we can see in the numerator where we have one minus the cosine of our angle A is 11 B. And it holds true for the denominator where we have one plus the cosine of that same angle A which remains 11 B. So we can say that A equals 11 B. And we can use substitution for that right hand side of the equation where the tangent of A divided by two, that's our simplified expression. So we know that A equals 11 B, we can rewrite. The tangent of A divided by two is the tangent of what A is equal to 11 B still divided by two. That doesn't simplify anymore. So that's our simplified expression. The tangent of 11 B divided by two, we look at our answer choices and that matches with answer choice D well done. We'll catch you on the next one.

Struggling with Trigonometry?

Simplify each expression.
±√[(1 - cos 5A)/(1 + cos 5A)]

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Double Angle Identities practice set

Struggling with Trigonometry?

Simplify each expression.±√[(1 - cos 5A)/(1 + cos 5A)]

Watch next

Double Angle Identities practice set

Simplify each expression.
±√[(1 - cos 5A)/(1 + cos 5A)]