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If 5sin + 3cos = 5, then how to prove that 3sin – 5cos = _+3

If 5sin + 3cos = 5, then how to prove that 3sin – 5cos = _+3

Grade:10

1 Answers

Akhil Chinnu
45 Points
5 years ago
Given,5sin+3cos=5 and let 3sin-5cos=x
square the both equations,
25sin²+9cos²+30sincos=25 and 9sin²+25cos²-30sincos=x²
add both equations,34(sin²+cos²)=25+x²
which is equal to34=25+x²
x²=9
x=_+3

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