Question

a cos θ—b sin θ=x and a sin θ+b cos θ=y, a^2+b^2 =

Answer 1

Answer:

x=asinθ+bcosθ

y=acosθ−bsinθ

Now,

x

2

+y

2

=a

2

+b

2

+2absinθcosθ−2absinθcosθ

x

2

+y

2

=a

2

+b

2

hence,proved.

Answer 2

Answer:

x=asinθ+bcosθ

y=acosθ−bsinθ

Now,

x

2

+y

2

=a

2

+b

2

+2absinθcosθ−2absinθcosθ

x

2

+y

2

=a

2

+b

2

hence,proved.