Core 3: Find all the solutions of 2cos(2x) = 1-2sin(x) in the interval 0<x<360

2cos(2x) = 1-2sin(x)

2(1-2sin2(x)) = 1-2sin(x) -- by our trigonometric functions

2-4sin2(x) = 1-2sin(x)

4sin2(x)-2sin(x)-1=0 -- rearrange

sin(x) = (2±(4-4(4)(-1))0.5)/8 -- quadratic formula

x = 54 & x = -18 which on the range 0

Answered by Chris B. Maths tutor

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