SOLUTION: verify sin(3x)=sinx(4cos^2x-1)

Algebra ->  Trigonometry-basics -> SOLUTION: verify sin(3x)=sinx(4cos^2x-1)      Log On


   

Question 1056706: verify sin(3x)=sinx(4cos^2x-1)
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
using identities, we have:
sin(3x) = sin(2x+x) = sin(2x)cos(x) + sin(x)cos(2x)
and sin(2x) = 2sin(x)cos(x); cos(2x) = 2cos^2(x) - 1
so sin(3x) = 2sin(x)cos(x)*cos(x) + sin(x)(2cos^2(x) - 1) -> sin(x)(2cos^2(x)+2cos^2(x) - 1) -> sin(x)(4cos^2(x)-1)