Question

rewrite in terms of sin x cos x.

Sin 4x

Answer 1

sin (4x) = sin (2x + 2x)
= sin (2x) cos(2x) + sin (2x)cos(2x)
= 2 sin(2x)cos(2x)

I used the formula for sin (A+B) = sin A cos B + sin B cos A

so A = 2x and B = 2x in this problem

Answer 2

@Easyaspi314 is right but you need to again expand sin 2x and cos 2x using formulae sin(x+x) and cos(x+x)

Answer 3

OpenHware..I dont believe that was the intent of the question...as cos(2x) will never be just in six or cos x...best scenario is cos^2x or sin^2x

Answer 4

yeah (cos x) ^2 and (sin x)^2 are still in terms of cos x and sin x.............and I believe the question was to breakdown the given expression in terms of cos x and sin x

Answer 5

The problem didnt specify. So I think it is fine.

Answer 6

We can't split hairs or second-guess without specifically stating sin x or/and cos x ONLY.

Answer 7

and cos(2x) is technically also in terms of cos x, just like cos^2(x) is in terms of cos x.