sin-16x-sin-x-pls-help-

Question Number 29821 by Victor31926 last updated on 12/Feb/18

\frac{\sin 16 x}{\sin x} ? pls help .

Commented by abdo imad last updated on 13/Feb/18

w h a t i s t h e q u e s t i o n ?

Commented by MJS last updated on 14/Feb/18

\frac{\sin 2 n x}{\sin x} = 2 \underset{i = 1}{\sum^{n}} \cos (2 i - 1) x

\frac{\sin (2 n - 1) x}{\sin x} = 1 + 2 \underset{i = 1}{\sum^{n - 1}} \cos 2 i x

Commented by Rasheed.Sindhi last updated on 14/Feb/18

\frac{\sin (2^{n} x)}{\sin x} = 2^{n} \cos x \cos 2 x \cos 4 x \dots \cos 2^{n - 1} x

= 2^{n} \underset{k = 0}{\overset{n - 1}{Π}} \cos 2^{k} x

Answered by Rasheed.Sindhi last updated on 12/Feb/18

\frac{\sin 16 x}{\sin x} = \frac{2 \sin 8 xcos 8 x}{sinx}

= \frac{2 (2 \sin 4 xcos 4 x) \cos 8 x}{sinx}

= \frac{4 (2 \sin 2 xcos 2 x) \cos 4 xcos 8 x}{sinx}

= \frac{8 (2 sinxcosx) \cos 2 xcos 4 xcos 8 x}{sinx}

= \frac{16 \overset{\times}{sinx c o s x c o s 2 x c o s 4 x c o s 8 x}}{\overset{\times}{sinx}}

= 16 cosxcos 2 xcos 4 xcos 8 x

Commented by Victor31926 last updated on 12/Feb/18

thnks a lot \dots are u sure of the answer sir ?