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If 3 sinθ + 4 cosθ = 5, then the value of 4 sinθ – 3 cosθ is

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If 3 sinθ  + 4 cosθ  = 5, then the value of 4 sinθ  – 3 cosθ  is 

(1) –5 

(2) –2 

(3) 1 

(4) 0

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Correct option (4) 0

Explanation:

3sinθ  + 4 cosθ  = 5

9(1-cos2θ) + 16(1-sin2θ) + 24 sinθ cosθ = 25

25 - (9 cos2θ + 16 sin2θ-24 sin θ cosθ) = 25

(3cosθ - 4 sinθ)2 = 0

4 sinθ - 3 cosθ= 0

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