Question

If a cos theta + b sin theta is equal to m and a sin theta minus b cos theta is equal to n

Answer 1

Answer:

m^2+n^2=a^2+b^2;

Step-by-step explanation:

m=a sinθ + b cosθ;

n=acosθ-bsinθ;

Squaring the two equations we get

m^2=a^2 sin^2θ +b^2 cos^2θ +2asinθbcosθ

n^2=a^2cos^2θ-b^2sin^2θ-2acosθbsinθ

Adding the two

m^2+n^2=a^2sin^2θ+a^2cos^2θ+b^2cos^2θ-b^2sin^2θ

m^2+n^2=a^2(1)+b^2(cos^2θ+1-cos^2θ)

m^2+n^2=a^2+b^2;