Question

Use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine,
cos4 x sin2 x

Answer 1

yes

Answer 2

well for starters you could split cos^4 to cos^2 * cos^2

Answer 3

cos^2 x is an identity

Answer 4

http://www.purplemath.com/modules/idents.htm

Answer 5

Can you do it from there?
Sin^2 and cos^2 break down

Answer 6

sin^2 cos^2= 1/4 sin^2(2x) = 1/4 (1- cos (4x))/2 so the final answer 1/8(1-cos4x) ?

Answer 7

Nope, there's much more work to be done.
\[\begin{align*}
\cos^4x\sin^2x&=(\cos^2x)^2\sin^2x\\\\
&=\left(\frac{1+\cos2x}{2}\right)^2\left(\frac{1-\cos2x}{2}\right)\\\\
&=\frac{1}{8}(1+\cos2x)^2(1-\cos2x)\\\\
&=\frac{1}{8}(1+\cos2x)(1-\cos^22x)\\\\
&=\frac{1}{8}(1+\cos2x)\left(1-\frac{1+\cos4x}{2}\right)\\\\
&=\frac{1}{16}(1+\cos2x)(1-\cos4x)\\\\
&=\frac{1}{16}(1+\cos2x-\cos4x-\cos2x\cos4x)
\end{align*}\]
I would say that the last term isn't exactly a first-power cosine term, since it's the product of two cosine factors. You can rewrite it using another identity,
\[\cos(x+y)+\cos(x-y)=2\cos x\cos y\]