Question #9e5bf

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Answer 1 · 2017-04-12T19:16:00

Please see the explanation

Given: $2sin^2(theta) =2+cos(2theta)$

Use the identity $1 -2sin^2(theta)=cos(2theta)$ :

$2sin^2(theta) =2+1 -2sin^2(theta)$

Add $2sin^2(theta)$ to both sides:

$4sin^2(theta) =3$

$sin^2(theta) = 3/4$

$sin(theta) = +-sqrt(3)/2$

From 0 to $2pi$

$theta = pi/3, (2pi)/3, (4pi)/3, and (5pi)/3$