SOLUTION: trigonometric equations: Solve: 1)sin^2x-4sinx+2=0 2)2sin^2x-cos2x=0

Question 756998: trigonometric equations:
Solve: 1)sin^2x-4sinx+2=0
2)2sin^2x-cos2x=0

Answer by dkppathak(439) (Show Source): You can put this solution on YOUR website!
1)sin^2x-4sinx+2=0 let sin x =y
y^2-4y+2=0
by completing perfect square we will factorize the equation
y^2-4y+(2)^2-(2)^2+2=0
y^2-4y+4-4+2=0
y^2-4y+4-2=0
(y-2)^2-(sqrt2)^2=0
(y-2-sqrt2)(y-2+sqrt2)=0
y=2+sqrt2 or y=2-sqrt2
sin x=2+sqrt2 or sin x=2-sqrt2 let 2+sqrt2=v1 and 2-sqrt2=v2
x=2n pie+(-1)^n v1 or x=2n pie +(-1)^n v2

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