Question
If 7sin²θ + 3cos²θ = 4, then find
the value of θ?Solution
7sin²θ + 3cos²θ = 4sin²θ + 3sin²θ+3cos²θ = 4 4sin²θ + 3(sin²θ + cos²θ) = 4 4sin²θ + 3 (1) = 4 4sin²θ = 4 - 3 = 1 4sin²θ = 1 sin²θ = 1/4 → sinθ = 1/2 sin30° = 1/2 Hence, θ = 30°
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