Please answer this query as fast as possible and please dont answer in links solve the answer - Maths - Introduction to Trigonometry

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Please answer this query as fast as possible and please dont answer
in links solve the answer

Neha Sethi · Accepted Answer

Dear student
Given:5sinθ+3cosθ=4  
1To find: 3sinθ-5cosθConsider, 5sinθ+3cosθ2+3sinθ-5cosθ2=25sin2θ+9cos2θ+30sinθcosθ+9sin2θ+25cos2θ-30sinθcosθ=34sin2θ+34cos2θ=34sin2θ+cos2θ   As sin2θ+cos2θ =1=34⇒5sinθ+3cosθ2+3sinθ-5cosθ2=34⇒42+3sinθ-5cosθ2=34   using 1⇒3sinθ-5cosθ2=34-16⇒3sinθ-5cosθ2=18⇒3sinθ-5cosθ=±32
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Please answer this query as fast as possible and please dont answer in links solve the answer.