Question

If a cos 0 + b sin 0 = p, a sin 0- b cos 0 = q then​

Answer 1

Answer:

Given : acosθ+bsinθ=m   ---( 1 )

            asinθ−bcosθ=n    ---( 2 )

Squaring (1) and (2), we get

a  

2

cos  

2

θ+b  

2

sin  

2

θ+2absinθcosθ=m  

2

    ---(3)

and  

a  

2

sin  

2

θ+b  

2

cos  

2

θ−2absinθcosθ=n  

2

   ---(4)

Adding (3) and (4)

a  

2

(sin  

2

θ+cos  

2

θ)+b  

2

(sin  

2

θ+cos  

2

θ)=m  

2

+n  

2

 

or  

a  

2

+b  

2

=m  

2

+n  

2