Question

If ( 3 sin theta + 5 cos theta ) = 5 then the value of ( 5 sin theta + 3 cos theta) is ?​

Answer 1

Answer:

Given,3sinθ+5cosθ=5

Let,5sinθ−3cosθ=x

Squaring on both sides for both the equations

⇒9sin^2θ+25cos^2θ+30sinθcosθ=25

⇒25sin^2θ+9cos^2θ−30sinθcosθ=x^2

Adding the equations ;

⇒34(sin^2θ+cos^2θ)=25+x^2

⇒x^2 = 34−25 = 9

⇒x=±3

∴5sinθ−3cosθ=±3

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