Question

solve questions number -20

Answer 1

Hello,
(asinθ -bcosθ)²+(acosθ+bsinθ)²;
=a²sin²θ-2absinθcosθ+b²cosθ²+(a²cos²θ+2absinθcosθ+b²sin²θ);
=a²sin²θ-2absinθcosθ+b²cosθ²+a²cos²θ+2absinθcosθ+b²sin²θ;
=a²sin²θ+b²cosθ²+a²cos²θ+b²sin²θ;
=a²(sin²θ+cos²θ)+b²(sin²θ+cos²θ)
for the fundamental relationship sin²θ+cos²θ=1:
=a²(1)+b²(1);
=a²+b²

then (asinθ -bcosθ)²+(acosθ+bsinθ)²=a²+b²

bye :-)