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I'm stuck on two trigonometry questions.

One requires me to prove a trigonometry summation and the other requires me to find the general solution of the given equation.

1. I am required to prove the b/m

**sin x + sin 2x + sin 3x + ... + sin nx = {sin (n/2)x sin [(n+1)/2]x}/ sin (x/2)**

I've attempted to prove this using mathematical induction. However, I'm stuck and need help/ advice on how I should proceed further. Attached is the work I have done so far.

View attachment 279

2. I have to find the general solution of the following equation:

**tan (2x - pi) = sin x**

I've been able to get till

**tan 2x = sin x**. However, whatever I've done after that doesn't give me the correct solution, which is

**.**

x = n*pi or 2n*pi

x = n*pi or 2n*pi

__+__1.946Your help/ advice will be greatly appreciated.

Thanks in advance.