The sum of all values of ∈ [0 ,2 ] satisfying 2 sin^2 = cos2 and 2 cos^2 =3 sin is.

Question

Accepted Answer

Correct answer: C. (c) 2 sin^2 ⁡ = cos ⁡2 2 sin^2 =1-2 sin^2 ⁡ 4 sin^2 =1 sin^2 ⁡ = 14 sin ⁡ = 12 2 cos^2 ⁡ =3 sin ⁡ 2-2 sin^2 ⁡ +3 sin ⁡ -2=0 (2 sin ⁡ -1 ) (2 sin ⁡ -2 )=0 sin ⁡ = 12so common equation which satisfy both equations is sin ⁡ = 12 = 6 , 5 6 ( ∈ [0 ,2 ] ) Sum =

$The sum of all values of θ \in [0, 2 π] satisfying 2 sin^{2} θ = cos 2 θ and 2 cos^{2} θ = 3 sin θ is.$

Solution

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