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Question

The general solution of the equation 7 cos2 θ+3 sin2 θ=4 is
(a) θ=2 nπ±π6, n Z

(b) θ=2 nπ±2π3, n Z

(c) θ=nπ±π3, n Z

(d) none of these

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Solution

(c) θ=nπ±π3, n Z
Given:

7 cos2 θ + 3 sin2θ = 4 7 cos2θ + 3 (1 - cos2θ) = 4 7 cos2θ + 3 - 3 cos2θ = 4 4 cos2θ + 3 = 4 4 (1 - cos2θ) = 34 sin2θ = 3 sin2θ = 34 sin θ = 32 sin θ = sin π3 θ = nπ ±π3, n Z

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