In Exercises 35–38, use the power-reducing formulas to rewrite ea...

Question

In Exercises 35–38, use the power-reducing formulas to rewrite each expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1.

sin² x cos² x

Accepted Answer

Hello, everyone. We are asked to rate the given expression into a trigonometric function with a power equal to one with the help of power reducing formulas. The expression we are given is for sine squared X cosine squared X. There are four answer choices. The first thing I noticed about the expression we are given is that it reminded me of the formula two sine X cosine X. And that's the formula for the sign of two X. How this helps us is four sine squared X cosine squared X is the same as two sine X cosine X squared. So now that I've rewritten this, I can substitute in the sign of two X for two sine X cosine X. So now in parentheses, I have the sign of two squared, I'm going to square the sign, it will not affect the angle. So this will now be the sign squared of two X. And I recall that the sine squared of X formula is one minus the cosine of two X divided by two. So I'm gonna put that in and then I'm going to double the angle because we are working with sine squared two X not just sine squared of one X. So this would be one minus the cosine of four acts divided by two because I doubled the angle from what our original identity was. I doubled the angle in my steps. And this looks like our answer. Everything's in terms of a power of one and I don't think it can go any further. So one minus the cosine of four X divided by two is our answer and it is answer choice B have a nice day.

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In Exercises 35–38, use the power-reducing formulas to rewrite each expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1. sin² x cos² x