The value of tan^{-1} c1x-y / c1y+x + tan^{-1} c2-c1/1+c1c2

Question

The value of \(tan^{-1} \frac{c_1x-y}{c_1y+x} + tan^{-1}\frac{c_2 - c_1}{1 + c_1c_2} + tan^{-1}\frac{c_3 - c_2}{1 + c_2c_3} + ......+ tan^{-1} \frac 1{c_n}\) is 

(a) \(tan^{-1} \frac xy\)

(b) \(tan^{-1} \frac yx\)

(c) tan^–1x – tan^–1y

(d) None

Answer 1

Correct option is (a) \(tan^{-1} \frac xy\) 

Write the series as