Question

sin(n + 1)x sin(n + 2).x + cos(n+1)
x cos(n +1)x cos(n + 2)x = COS X
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Answer 1

Step-by-step explanation:

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

it is from the identity

cos(a-b) = cosa * cosb + sina * sinb

here a= (n+1)x b= (n+2)x

so,

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

cos(nx+x-nx-2x)

cos(-x)  

cosx { since cos(-x) = cosx }