Question

Sin(n+1)x sin(n+2)x+cos(n+1)x cos(n+2)x=cosx

Answer 1

Step-by-step explanation:

if we take (n+1)x=a and (n+2)x=b

the above expression is in the form of :

sinasinb+cosacosb which is equal to cos(a-b)

in cos(a-b) substitute a and b

=cos[(n+1)x - (n+2)x]

=cos[nx+x-nx-2x]

=cos(x-2x)

=cos(-x)

=cos(x). (because cos of any negative value is the same value as it's positive value)

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feel free to comment if u have any doubts.