Q. 245.0( 8 Votes )

# If θ_{1}, θ_{2}, θ_{3}, …, θ_{n} are in AP, whose common difference is d, show that

Answer :

Given: θ_{1}, θ_{2}, θ_{3},…, θ_{n} is A.P

∴ θ_{2} – θ_{1} = θ_{3} – θ_{2} = θ_{4} – θ_{3} =…………= θ_{n} – θ_{n-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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