solve for x sin2x2 15cosx sin2x 05Solutionsin2x2 15cosx

solve for x.

sin^2(x/2) + 1.5cos(x) = sin(2x) + 0.5

Use the Trig. formula : cos2y = 1 - 2sin^2y

(1-cosx)/2 + 1.5cosx = sin2x +0.5

0.5 -0.5cosx +1.5cosx = sin2x +0.5

cosx = sin2x

cosx -sin2x =0

cosx -2sinxcosx =0

cosx( 1- 2sinx) =0

Solution I : cosx = 0

General solutions : x = pi/2 + 2k*pi and x = 3pi/2 + 2k*pi

Solution II : sinx = 1/2

General solution : x = pi/6 + 2k*pi and x = 5pi/6 + 2k*pi