Trigonometry?

Question

Prove this identitys:
1.sin 8(a)=8*sin(a)*cos(a)*cos(2a)*cos(4a)
2.cos 3(a)=4*cos^3(a)-3*cos(a)

you can also just tell me the steps I have to take in each question

Answer 1

use sin(2a) = 2sin(a)cos(a)

sin(8a) = 2sin(4a)cos(4a)
= 4sin(2a)cos(2a)cos(4a)
=8sin(a)cos(a)cos(2a)cos(4a)

cos(a+b) = cos(a)cos(b) - sin(a)sin(b)
cos(3a) = cos(a+2a)= cos(a)cos(2a) - sin(a)sin(2a)
= cos(a)(2cos^2(a) -1) - 2sin^2(a)cos(a)
=2cos^3(a) - cos(a) - 2(1-cos^2(a))cos(a)
=4cos^3(a) - 3cos(a)