# If θ1,

Given: θ1, θ2, θ3,…, θn is A.P

θ2 – θ1 = θ3 – θ2 = θ4 – θ3 =…………= θn – θn-1 = d (Common Difference)

Now,

Multiplying and dividing by sin d:

{ sin(A - B) = sin A cos B - cos A sin B}

Similarly,

Take L.H.S.:

Putting the value of (i), (ii) and (iii):

= R.H.S.

Hence Proved

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