Question

If (3 sin 0+5 cos 0) = 5, prove that (5 sin 0 - 3 cos 6) = plus minus 3.​

Answer 1

Given 3sinθ+5cosθ=5

Let 5sinθ−3cosθ=x

Squre both sides of both the equations :-

⇒9sin² θ+25cos²θ+30sinθcosθ=25 ....Eq1

&

⇒25sin² θ+9cos² θ−30sinθcosθ=x²......Eq2

Adding the equations Eq1 &Eq2 :

⇒34(sin²θ+cos²θ)=25+x²

⇒x²=34−25=9

⇒x=±3

∴5sinθ−3cosθ=±3 (proved)