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

Question

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!

1013 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-10-15T18:52:43

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

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)#