Question

Rewrite with only sin x and cos x.

sin 3x

Answer 1

sin3x = sin(2x+x) = ?

use formzula sin(a+b) = ?

Answer 2

\(\sin (x+y) = \sin x \cos y + \cos x \sin y\)

\(\sin 3x=\)

\(= \sin (x + 2x)\)

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

Now use the sine of 2x and the cosine of 2x to simplify further.

Answer 3

The answer is 2cos^2x sinx + sinx - 2sin^3x?

Answer 4

Also, \(\cos (2x) = \cos^2 x - \sin ^2 x\)


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

\(=\sin x (\cos^2 x - \sin ^2 x) + 2\cos x \sin x \cos x\)

\(=\sin x \cos^2 x - \sin^3 x + 2 \sin x \cos^2 x \)

\(= 3\sin x \cos^2 x - \sin^3 x\)

Answer 5

You are also correct.

Answer 6

Thanks.

Answer 7

yw