(sin^2x)(cos^2x) use power reducing formulas to write the expression in terms of the first power of cosine

Question

loser66 · Answer

$$sin^2x = \frac{1-cos2x}{2}$$
$$cos^2x=\frac{1+cos2x}{2}$$
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$$sin^2x *cos^2x = timethemtogether$$

anonymous · Answer

@Loser66 but don't you get cos^2 again?

loser66 · Answer

I know what you mean but why do you expand them to get that form? let (...)*(...) . so? no power there, right?

anonymous · Answer

@Loser66 so does it become cos4x instead of what I was thinking like... 2cos^2x?

loser66 · Answer

or if you dare not trap your prof like what I did, you can expand them, and then use the power reduce again.

loser66 · Answer

$$(\frac{1+cos2x}{2})*(\frac{1-cos2x}{2})=\frac{1}{2}*(1-cos^22x)$$
now, replace again by the trig of $$cos^2(2x) = \frac{1+cos(4x)}{2}$$
can you step up from here?

loser66 · Answer

$$\frac{1}{2} * (1 - \frac{1+cos (4x)}{2})$$got what I mean, friend?

anonymous · Answer

@Loser66 yeah thanks!

loser66 · Answer

good, but didn't get a beautiful answer yet, need some more steps to simplify it. I don't think it's hard to you. when I trapped my prof, he got mad at me but then, we were closer.