Question

Use the squared identities to simplify 2sin2x cos2x. Check below.

Answer 1

Answer:

$2\sin^2 x\cos^2 x=\frac{1-(\cos 2x)^2}{2}$

Step-by-step explanation:

Given : Expression - $2\sin^2 x\cos^2 x$

To simplify : The given expression?

Solution :

Expression - $2\sin^2 x\cos^2 x$

Apply the squared identity of the trigonometric function,

$\sin^2 \theta=\frac{1-\cos 2\theta}{2}$

$\cos^2 \theta=\frac{1+\cos 2\theta}{2}$

Substitute the value in the given expression,

$=2\sin^2 x\cos^2 x$

$=2\times \frac{1-\cos 2x}{2}\times \frac{1+\cos 2x}{2}$

$=\frac{(1-\cos 2x)(1+\cos 2x)}{2}$

Apply,  $a^2-b^2=(a+b)(a-b)$

$=\frac{1^2-(\cos 2x)^2}{2}$

$=\frac{1-(\cos 2x)^2}{2}$

Therefore, $2\sin^2 x\cos^2 x=\frac{1-(\cos 2x)^2}{2}$

Answer 2

To simplify 2sin2x cos2, you need to use (1 - cos(4x))/4. The correct answer between all the choices given is the first choice or letter A. I am hoping that this answer has satisfied your query about and it will be able to help you.