sin(n+1)xsin(n+2)+cos(n+1)xcos(n+2)x =cosx
Answers
Answered by
11
LHS
sin(n+1)xsin(n+2)+cos(n+1)xcos(n+2)x
= cos(n+1)xcos(n+2)x+sin(n+1)xsin(n+2)
= cos[(n+1)x-(n+2)x] [ using cos(A-B) = cosAcosB+sinAsinB ]
= cos[nx+x-nx-2x]
= cos(-x)
= cosx [ since cos(-θ) = cosθ ]
RHS Hence Proved
Similar questions