Question

How do you simplify `1-4sin^2xcos^2x`?

Answer 1

It can be simplified to `cos^2(2x)` or `1/2(cos4x+1)`

Explanation:

We have that

`1-4sin^2x*cos^2x=(1^2-(2cosx*sinx)^2)=(1-(sin2x)^2)=cos^2(2x)`

Also we know that

`cos(4x)=2*cos^2(2x)-1=>cos^2(2x)=1/2(cos4x+1)`

Remarks

It is known that : `sin^2(2x)+cos^2(2x)=1`