Question

How do you use the power reducing formulas to rewrite the expression `sin^2xcos^4x` in terms of the first power of cosine?

Answer 1

`((sin^2 2x)(1 + cos 2x))/8`

Explanation:

Use trig identities:
sin 2a = 2sin a.cos a
`cos^2 a = (1 + cos 2a)/2`
In this case:
`f(x) = sin^2 x.cos^4 x = sin^2 x.cos^2 x(cos^2 x)`
Because,
`sin^2 x.cos^2 x = (sin^2 2x)/4` and
`cos^2 x = (1 + cos 2x)/2`
There for:
`f(x) = (sin^2 2x(1 + cos 2x))/8`