Question

2.) If x cos A + y sin A = m and
x sin A - y cos A = n, then prove that :
x² + y2 = m² + n²​

Answer 1

Step-by-step explanation:

m^2+n^2 =(x cos A+y sin A)^2+(x sin A−y cos A)^2

m^2+n^2=x^2 cos^2 A+y^2 sin^2A+2xy cosAsinA+x^2sin^2A+y^2cos^2A−2xy sinAcosA

m^2+n^2=x^2(cos^2A+sin^2A)+y^2(sin^2A+cos^2A)

m^2+n^2=x^2+y^2   [Since, cos^2A+sin^2A=1]