Simplify each expression.
± √[(1 + cos (x/4))/2...

Question

Simplify each expression.

± √[(1 + cos (x/4))/2]

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. Then inside of the radical, we have a fraction in the numerator of that fraction, we have one plus the cosine of X divided by 10. And then in the denominator of that fraction, we have two. Our answer choices are answer choice. A two cosine of X divided by 20 answer choice B the cosine of X divided by 20 answer choice C the cosine of X divided by five and answer choice D two sine of X divided by five. All right, recalling from previous lessons on trigonometric identities and looking at those tables in the textbook, we see that this looks a lot like a half angle identity. Specifically the one that has plus or minus the square rut of. And then inside of that radical, we've got a fraction in the numerator of that fraction. We have one plus the cosine of A and that's all divided by two. That whole thing is equal to the cosine of a divided by two, our half angle identity So here we can compare our given trigonometric expression with our trigonometric identity and see that our angle A is equal to X divided by 10. So we can set that A equals X divided by 10. And then use substitution to plug into the right side of our half angle identity where the cosine of A divided by two becomes the cosine of instead of A that's X divided by 10 divided by two. Now, all we need to do is simplify this. If this part might be tripping you up X divided by 10, divided by two, you can rewrite that with a division symbol. Recalling that dividing two fractions is the same as multiplying by the reciprocal of the second fraction. So we have X divided by 10 multiplied by one half which will get us X divided by 20. So that's where we get our simplified expression. The cosine of X divided by 20 we look at our answer choices and that matches with answer choice. B well done. We'll catch you on the next one.

Struggling with Trigonometry?

Simplify each expression.
± √[(1 + cos (x/4))/2]

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Double Angle Identities practice set

Struggling with Trigonometry?

Simplify each expression.± √[(1 + cos (x/4))/2]

Watch next

Double Angle Identities practice set

Simplify each expression.
± √[(1 + cos (x/4))/2]