CBSE BOARD X, asked by joahnaraichel, 1 year ago

3sintheta + 5costheta = 5 , prove that 5sintheta - 3 costheta =+/- 3

Answers

Answered by pranavsk1525
8

Squaring on both sides


3sinθ+5cosθ)²= 5²


(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

Answered by priyakonnothjp
2

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