Simplify each expression.
±√[(1 + cos 18x)/2]

Question

Simplify each expression.

±√[(1 + cos 18x)/2]

Accepted Answer

Welcome back. I am so glad you're here. We are asked to use a trigonometric identity to simplify the expression. Our given expression is plus or minus the square of and inside of the radical, we have a fraction in the numerator. We have one plus the cosine of 98 X and that's divided by two. Our answer choices are answer choice. A sign of 198 X. Answer trace B, the sign of 49 X, answer trace C the tangent of 49 X and answer choice D the cosine of 49 X. All right. So looking at this expression, it looks a lot like one of our half angle identities, particularly particularly the one where we have plus or minus the square root of and inside the radical, we have a fraction in the numerator of that fraction. We have one plus the cosine of A and that's all divided by two. And that whole thing is equal to the cosine of a divided by two. And we can see here that our given expression matches the left half of that half angle identity almost perfectly. The only difference is that we have this A and in the given expression that A would be equal to 98 X. So we can set our expression equal to in the right hand side of the trigonometric I or half angle identity, which would be the cosine of. And instead of A, that will be a 98 X divided by two. And now all we have to do is simplify the right hand side, 98 X divided by two is going to be 49 X. So this simplifies to be the cosine of 49 X. And there we have simplified our expression, we look at our answer choices and this matches with answer choice. D well done. We'll catch you on the next one.

Struggling with Trigonometry?

Simplify each expression.
±√[(1 + cos 18x)/2]

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Double Angle Identities practice set

Struggling with Trigonometry?

Simplify each expression.±√[(1 + cos 18x)/2]

Watch next

Double Angle Identities practice set

Simplify each expression.
±√[(1 + cos 18x)/2]