if 5 sin theta + 3 cos theta = 4 , find the value of 3 sin theta - 5 cos theta
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the answer is -4
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Answer:
5 SIN Q + 3 COS Q = 4
5 SINQ = 4-3 COS Q
==> SINQ = 4-3 COSQ/5...(1)
AND
5 SIN Q + 3 COS Q = 4
==> 3 COSQ = 4-5SINQ
==> COSQ = 4-5 SINQ/3 ...(2)
WE FIND
3 SIN Q - 5 COS Q ...(3)
PUTTING VALUE OF SINQ IN EQ(3)
==> 3(4-3 COSQ/5) - 5 COSQ
==> 12 - 9 COSQ / 5 - 5 COSQ
==> 12-9COSQ - 25 COSQ / 5
==> 12 - 34 COSQ / 5
==> 2(6- 17 COSQ )/5
ITS ALSO SOLUTION
ITS ANOTHER STATEMENT BUT METHOD IS SAME
Similar questions
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
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