If x+2=4sinx for 0<x<(pi/2), express cos(2x) in terms of x. Cos(2x)=?

I'm assuming I have to use the cos(2x)=1-2((sin^2)x) relationship, but I'm stuck on how to rearrange everything to that I can get an equivalent equation and therefore find the answer. Detailed explanations are appreciated so I can do future problems like this confidently on my own!

1 Answer
Oct 15, 2017

cos2x=(x2+4x48)

Explanation:

Given x+2=4sinx

sinx=x+24
sin2x=(x+2)216

cos(2x)=12sin2x
cos2x=12(x+2)216=1(x+2)28
cos2x=8x24x48=(x2+4x48)