A Maths Trigonometry HELP!

Can you help me with the following two questions?

1. Prove the identity, (Sin A + Sin B)(Sin A - Sin B) = Sin(A + B)Sin(A - B)

2. Prove that Sin X + Sin 2X + Sin 3X + Sin 4X = 4 Cos X/2 Cos X Sin 5X/2.

Hence, find all the angles between 0 and pi for which

Sin X + Sin 2X + Sin 3X + Sin 4X = 0 (Ans: pi/2, 2pi/5, 4pi/5)

Thanks for helping me out! (:

Hi,

For Q1, start from LHS. You will need to use suitable factor formulae and double-angle formula.

For Q2, start from LHS and use a suitable factor formula three times. Use RHS expression to solve for X.

Thanks!

Cheers,
Wen Shih