If A and B are the solutions of the equation acosx + bsinx = c, then show that
1) sin (A+B) = 2ab/a²+b²
2)cos (A+B) = a^2-b²/a²+b²

also find tan(A+B)

Pu the values A and B in place of x to obtain 2 eqns. Subtract them to form an eqn and then obtain the relation between A and B (consider only principle soln.)

From the above eqn,., firstly, a relation between A and B will be obtained. Also, a relation between A,B and a,b will be obtained,

Use Cos 2x= (1-tan²x)/(1+tan²x) or any multiple angle identity to get ahead and arrive at the desired result.