Question

Use the​ power-reducing formulas to rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1.

16 sin4x
16sin4x = _____

Answer 1

`6-8cos2x+2cos4x`

Explanation:

We are given that

`16sin^4 x`

We can write the given expression as

`16(sin^2x * sin^2 x)`

`16((1-cos2x)/(2))((1-cos2x)/(2))`

By using the formula

`sin^2\theta=(1-cos2\theta)/(2)`

`4(1-cos2x)^2`

`4(1-2cos2x+cos^2(2x)`

Using the identity

`(a-b)^2=a^2+b^2-2ab`

`4(1-2cos2x+(1+cos4x)/(2))`

`4-8cos2x+2+2cos4x`

`6-8cos2x+2cos4x`

This is required expression.