Question

Use the squared identities to simplify 2sin^2 x cos^2 x

A. (1+4cos(2x)-cos(4x))/4
B. (1+4cos(2x)+cos(4x))/4
C. (1+cos(4x))/4
D. (1-cos(4x))/4

Answer 1

The given question is

`2sin^2 x cos^2 x`

Multiplying and divide by 2

`(4sin^2 x cos^2 x)/(2) =\frac{(2 sinx cos x})^2{2}=(sin^2(2x))/(2)`

Again multiplying and dividing by 2

`(2sin^2(2x))/(4)`

And

`2 sin^2(2x)=1-cos(4x)`

So we will get

`(1-cos(4x))/(4)`

Correct option is D