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

cos 2x = -((x^2+4x-4)/8)

Explanation:

Given x+2=4sin x

sin x= (x+2)/4
sin^2x = (x+2)^2/16

cos (2x) = 1 - 2sin^2x
cos 2x = 1 - (2*(x+2)^2) /16 = 1 - (x+2)^2/8
cos 2x = (8-x^2-4x-4)/8 = -((x^2+4x-4)/8)