Prove the following equation:
Will post question below.

Question

Prove the following equation:
Will post question below.

anonymous · Answer

$$\large \sin^2 \theta \cos^2 \theta = \frac{ 1 }{ 8 }(1-\cos 4\theta)$$

anonymous · Answer

@amistre64 can you please help me??

amistre64 · Answer

how to prove?  work left to right?

amistre64 · Answer

some things to keep in mind:

$$cos(2x)=cos^2(x)-sin^2(x)$$
$$cos(2x)=1-2sin^2(x)$$
$$cos(2x)=2cos^2(x)-1$$

amistre64 · Answer

$$2sin(x)cos(x)=sin(2x)$$

amistre64 · Answer

$$cos(4x)=1-2sin^2(2x)$$
$$2sin^2(2x)=1-cos(4x)$$
$$sin^2(2x)=\frac{1}{2}(1-cos(4x))$$
$$[2sin(x)cos(x)]^2=\frac{1}{2}(1-cos(4x))$$
$$4sin^2(x)cos^2(x)=\frac{1}{2}(1-cos(4x))$$
$$sin^2(x)cos^2(x)=\frac{1}{8}(1-cos(4x))$$
if you have to back into it that should give you some direction

anonymous · Answer

thank you very much!

amistre64 · Answer

youre welcome