sinx+sin2x+sin3x+...+sin nx=sin((n+1)/2)x .((sin nx)/2) / sin(x/2)

TPT :

step I : for n = 1

LHS =

RHS =

thus the result is true for n = 1.

Step II: let it is true for n = k.

therefore ..................(1)

now in the third step , we will try to prove that it is true for n = (k+1).

step III:

thus it is true for n = (k+1). therefore it will be true for all values of n belongs to N.

hope this helps you.

cheers!!

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