Q24 of 167 Page 19

If θ1, θ2, θ3, …, θn are in AP, whose common difference is d, show that

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


More from this chapter

All 167 →
22

The first and the last term of an A.P. are a and l respectively. Show that the sum of the nth term from the beginning and the nth term from the end is a + l.

 23

If an A.P. is such that find .

 1

The Sum of the three terms of an A.P. is 21 and the product of the first, and the third terms exceed the second term by 6, find three terms

 2

Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers