Question

Acosø+bsinø=m and asinø-bcos=n,then a²+b²=

Answer 1

Answer:

a²+b²=m²+n²

Explanation:

$Acos\theta+Bsin\theta=m\\(Acos\theta+Bsin\theta)^2=m^2\\A^2cos^2\theta+B^2sin^2\theta+2ABsin\theta cos\theta=m^2..................(i)\\\\Asin\theta-Bcos\theta=n\\(Asin\theta-Bcos\theta)^2=n^2\\A^2sin^2\theta+B^2cos^2\theta-2ABsin\theta cos\theta=n^2...................(ii)$

Adding (i) and (ii),

$A^2cos^2\theta+B^2sin^2\theta+2ABsin\theta cos\theta+A^2sin^2\theta+B^2cos^2\theta-2ABsin\theta cos\theta=m^2+n^2\\A^2(sin^2\theta +cos^2\theta)+B^2(sin^2\theta+cos^2\theta)=m^2+n^2\\A^2(1)+B^2(1)=m^2+n^2\\A^2+B^2=m^2+n^2$