Question

if p= a cos A + b sin A and q = a sinA - b cosA then show that= a^2 + b^2 = p^2 + q^2​

Answer 1

Answer:

Taking RHS

As , p=acosA +bsinA and q=asinA-bcosA

=p^2+q^2

=(acosA + bsinA)^2 +(asinA-bcosA)^2

=a^2cos^2A +b^2sin^2A +2absinAcosA +a^2sin^A +b^2cos^2A -2absinAcosA

=a^2cos^2A +a^2sin^2A +b^2sin^2A +b^2cos^2A

=a^2 (cos^2A +sin^2A) +b^2 (sin^2A +cos^2A)

Now, as sin^2A + cos^2A =1

=a^2+b^2

=LHS