Trigonometry

Question

sin (n + 1)x sin (n + 2)x + cos (n + 1)x cos (n + 2)x = cos prove it

Answer 1

A wel- known  angle subtraction formula is:

 

cos(A - B) =  cosA cosB + sinA sinB.

 

to prove the equation -   set B = nx + x  and A = nx  +2x

 

The A -B = x.     This is the right hand side.

The left hand side is sin (n + 1)x sin (n + 2)x + cos (n + 1)x cos (n + 2)x

This proves the assertation