Question

cos((n+1) A) cos((n+2) A) + Sin ( (n+1)A) Sin ((n+2)A)=cosA . prove that LHS=RHS​

Answer 1

Answer :

Solve LHS :-

=> we know that,

cos(A - B) = Cos A . CosB + SinA + SinB

Therefore ,

A = ( n + 1)x

B = (n +2)x

Hence,

sin(n + 1)x sin (n +2 )x + cos(n +1)x cos (n + 2)x

=> cos((n+1)x-(n+2)x)

cos(nx+x-nx-2x)

cos(-x)

cosx { since cos(-x) = cosx }

Proved