if 5sin +3cos=4 find the value of 3sin-5cos
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Answer:
3√2
Step-by-step explanation:
5 sinx + 3 cosx = 4
=> (5 sinx + 3 cosx)² = 4²
=> 25sin²x + 9cos²x + 30 sinx.cosx = 16
=> 25sin²x + 9cos²x = 16 - 30.sinx.cosx
consider, (3 sinx-5cosx)²
= 9sin²x+25cos²x-30sinx.cosx
= 9(1-cos²x)+25(1-sin²x) - 30sinx.cosx
= 9-9cos²x + 25 - 25sin²x - 30.sinx.cosx
= 34 - ( 25sin²x+9cos²x) - 30.sinx.cosx
= 34 - [ 16 - 30.sinx.cosx ] - 30sinx.cosx
= 34 -16 + 30.sinx.cosx - 30.sinx.cosx
= 18
=> (3 sinx-5cosx)² = 18
=> √(3 sinx-5cosx)² = √18
= √9*2 = 3√2
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