sin (n + 1)x sin (n + 2)x + cos(n + 1)xcos(n + 2)x = cosx.
sin (n + 1)x sin (n + 2)x + cos(n + 1)xcos(n + 2)x = cosx.
L.H.S = sin (n + 1)x sin (n + 2)x + cos(n + 1)xcos(n + 2)x
= cos[(n + 1)x - (n + 2)x]
= cos (-x)
= cosx
= RH.S
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= cot2x
cos(2
+x) 
= 1
= -
sinx