Question

If x =a sin + b cos and y = a cos +b sin then prove that x2+y2=a2+b2.
please answer fast.
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Answer 1

Answer:

x =a sin + b cos

y = a cos +b sin

Step-by-step explanation:

x =a sin + b cos ....1

y = a cos +b sin ....2

squaring and adding,we get

=x^2+y^2=a^2 cos^2x +b^2 sin^2x+2ab sinx Cosx +b^2 Cos^2x +a^2 sin^2-2ab sinx Cosx

=a^2(Sin^2x+Cos^2x)+b^2(sin^2x+Cos^2x)

=a^2+b^2

Hence,proved