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

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

Again multiplying and dividing by 2

$\frac{2sin^2(2x)}{4}$

And

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

So we will get

$\frac{1-cos(4x)}{4}$

Correct option is D