Answer :
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.
Answer:
[tex]2\sin^2 x\cos^2 x=\frac{1-(\cos 2x)^2}{2}[/tex]
Step-by-step explanation:
Given : Expression - [tex]2\sin^2 x\cos^2 x[/tex]
To simplify : The given expression?
Solution :
Expression - [tex]2\sin^2 x\cos^2 x[/tex]
Apply the squared identity of the trigonometric function,
[tex]\sin^2 \theta=\frac{1-\cos 2\theta}{2}[/tex]
[tex]\cos^2 \theta=\frac{1+\cos 2\theta}{2}[/tex]
Substitute the value in the given expression,
[tex]=2\sin^2 x\cos^2 x[/tex]
[tex]=2\times \frac{1-\cos 2x}{2}\times \frac{1+\cos 2x}{2}[/tex]
[tex]=\frac{(1-\cos 2x)(1+\cos 2x)}{2}[/tex]
Apply, [tex]a^2-b^2=(a+b)(a-b)[/tex]
[tex]=\frac{1^2-(\cos 2x)^2}{2}[/tex]
[tex]=\frac{1-(\cos 2x)^2}{2}[/tex]
Therefore, [tex]2\sin^2 x\cos^2 x=\frac{1-(\cos 2x)^2}{2}[/tex]