Question

If 4 sin theta + 3 cos theta = 3 find 3 sin theta - 4 cos theta.​

Answer 1

Answer:

0

Step-by-step explanation:

3sin θ+4cosθ = 5

Squaring both sides  

9sin  

2

θ+16cos  

2

θ+24sinθcosθ=25

9(1 cos  

2

=θ)+16(1−sinθ)+24sinθcosθ=25

9−9cos  

2

θ+16−16sin  

2

θ+24sinθcosθ=25

- 9 cos  

2

θ−16sin  

2

θ+24sinθcosθ=25916

9 cos  

2

θ+16sin  

2

θ−24sinθcosθ=0

(3cosθ4sinθ)  

2

=0

3cosθ−4sinθ=0

Alternate Method:

If ax+by=m  and ax−by=n

then (a  

2

+b  

2

)(x  

2

+y  

2

)=m  

2

+n  

2

 

Here  

a=sinθ

x = 3, m = 5,  and b = cos θ y = 4, n = ?

(sin  

2

θ+cos  

2

θ)(9+16)(5)  

2

+n  

2

 

n  

2

= 0, n = 0

3sinθ−4cosθ = 0