Question
If 5 sinθ + 3 cosθ = 4 then value of 5 cosθ - 3 sinθ = ?
Solution
If 5 sinθ + 3 cosθ = 4 Let 5 cosθ - 3 sinθ = K Then squaring both equation and adding (5sinθ+3cosθ)^2 = (4)^2 (5cosθ-3sinθ)^2 = (K)^2 25 sin²θ + 9 cos²θ+ 30 sinθ cosθ = 16 ---------------------------------------------- 9 sin²θ + 25 cos²θ- 30 sinθ cosθ = K² 34 sin²θ + 34 cos²θ = 16 + K² 34 (sin²θ + 34 cos²θ) = 16 + K²   { sin²θ + cos²θ = 1} 34 = 16 + K² K² = 34 - 16 = 18 K = √18 = ± 3√2
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