Question

If 3sin theta + 5 cos theta = 5 . prove that 5 sin theta- 3 cos theta = +- 3​

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