Question

please solve this questions ​

Answer 1

Given Question is

let theta = x

IF aCosx + bSinx = m

And

aSinx - bCosx = n

Find a²+b²

Solution:-

Squaring on b/s

a²Cos²x + b² Sin²x +2abCosx * Sinx = m²

a²Cos²x + b² Sin²x -m² = -2abCosx * Sinx .. Equation 01

Similarly

a²Sin²x + b²Cos²x -n² = 2abCosx * Sinx ... Equation 02

From Equation 01 and 02 we have

a²Cos²x + b² Sin²x -m² = -(a²Sin²x + b²Cos²x -n²)

a²(Cos²x + Sin²x ) + b²(Sin²x + Cos²x) = n²+m²

a²(1) + b²(1) = n²+m²

a² + b² = n²+m²

Therefore a² + b² = n² + m²