Question

1-cos(12x)= A. 2sin^2(6x) B. 2cos^2(6x) C. 2cos^2(12x) D. 2sin^2(12x)

Answer 1

Answer:  The correct option is (A). 2sin²(6x).

Step-by-step explanation: We are given the value of the following trigonometric expression:

$T_e=1-\cos(12x).$

We will be using the following trigonometric identity:

$1-\cos x=2\sin^2\dfrac{x}{2}.$

So, we have, using the above identity that

$T_e\\\\=1-\cos(12x)\\\\=2\sin^2\left(\dfrac{12x}{2}\right)\\\\=2\sin^2(6x).$

Therefore, the value of 1-cos(12x) is 2sin²(6x).

Thus, (A) is the correct option.

Answer 2

Cos(12x) = cos(6x+6x) = cos6xcos6x -sin6xsin6x = cos^2(6x) -sin^2(6x)

1 - cos(12x) = 1 - (cos^2(6x) -sin^2(6x)) = sin^2(6x) +cos^2(6x) - cos^2(6x) +sin^2(6x) = 2sin^2(6x)

so choice A. is right sure