Question

If 3sino + 5coso = 5, then the value
of 5sino - 3coso can be :

Answer 1

Given:

➡(3 sinθ+5cosθ)²= 5²

Squaring on both sides.

➡(3sinθ)²+(5cosθ)²+2× 3sinθ 5cosθ= 25

[a+b= a²+b²+2ab]

9sin²θ+ 25cos²θ+30sinθcosθ= 25

9 (1-cos²θ) + 25(1-sin²θ)+30sinθcosθ=25

➡[sin²θ + cos²θ =1]

➡9-9cos²θ + 25-25sin²θ +30sinθcosθ=25

➡9+25 -(9cos²θ +25sin²θ -30sinθcosθ) =25

34 - (9cos²θ +25sin²θ -30sinθcosθ) =25

➡- (25sin²θ +9cos²θ-30sinθcosθ) =25-34

(25sin²θ+9cos²θ -30sinθcosθ) =9

(5sinθ - 3cosθ)²= 9

(5sinθ - 3cosθ)= √9

(5sinθ - 3cosθ)= ±3

L.H.S = R.H.S

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