Question

A cos x - b sin x=c prove that a sinx+b cosx=+-square root a2+b2-c2

Answer 1

Acosx - bsinx = c ------(1)

take square both sides

a²cos²x + b²sin²x -2absinx.cosx = c² ----(1)

asinx + bcosx = L --------(2)

take square both sides

a²sin²x + b²cos²x +2absinx.cosx = L² ----(2)

add equations (1)and (2)

a²(sin²x + cos²x ) + b²( sin²x + cos²x ) = c² + L²

a² + b² = c² + L²

L² = a² + b² -c²

L = ±√( a² + b² - c²)

asinx + bcosx =±√(a² + b² - c²)

hence proved ///

Hope that this answer will help you ✌️