Question

If 3 sin A + 5 cos A=5 then show that 5 sin A - 3 cos A= +3.

Please provide full solution.
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Answer 1

Step-by-step explanation:

Given 3sinθ+5cosθ=5

Let 5sinθ−3cosθ=x

Squaring on both sides for both the equations

⇒9sin

2

θ+25cos

2

θ+30sinθcosθ=25

⇒25sin

2

θ+9cos

2

θ−30sinθcosθ=x

2

Adding the equations ;

⇒34(sin

2

θ+cos

2

θ)=25+x

2

⇒x

2

=34−25=9

⇒x=±3

∴5sinθ−3cosθ=±3

Hence proved

Answer 2

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