Question

how would you solve: sin(2x)+cos(2x)=tan(x)?

Answer 1

sin(2x)+cos(2x)=tan(x)
cos(2x) = sinx/cosx - 2sinxcosx
cos(2x) = (sinx - 2sinxcos^2x)/cosx
cos(2x) = sinx(1 - 2cos^2x)/cosx
cos(2x) = tanx(-cos(2x))
-1 = tanx
x = 135º or x = 315º
or in radians
x = 3pi/4 or 7pi/4

Answer 2

2 sinx cosx + cos^2x - sin^2x
= sinx/cosx
2 sinx cos^2x + cos^2x - sin^2x = sin x
2 sinx(1-sin^2x)+ (1-2sin^2x) = sinx
Treat sinx as the variable (u) and solve the polynomial
2 u(1 - u^2)+ 1 - 2u^2 = u
-2u^3 -2u^2 + u +1 = 0

Answer 3

My answer is wrong in the second line and what follows. Go with Reiny's