Question

3 sin( theta)+ 5 cos(theta) = 5, ,find the value of sin(theta) cos(theta), tan(theta)​

Answer 1

Answer:

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