Question

If 3 sin A + 5 cos A = 5 then show that 5 sin A - 3 cos A = ±3

Answer 1

HELLO DEAR,



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




I HOPE IT'S HELP YOU DEAR,
THANKS