Question

F 3 sin
+5 cos 8 = 5, prove that 5 sin 8- 3 cos 8 = +3.​

Answer 1

Answer:

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Step-by-step explanation:

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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Hope this will help you..‼️‼️‼️

Answer 2

Step-by-step explanation:

(3sin+5cos)^2=25

9sin^2+30sincos+25cos^2=25

9(1-cos^2)+30sincos+25(1-sin^2)=25

9-9cos^2+30sincos+25-25sin^2=25

9cos^2-30sincos+25sin^2=9

(3cos-5sin)^2=9

3cos-5sin=-3

5sin-3cos=3