$ an^{- 1}{\frac{c_{1}x - y}{c_{1}y + x} + an^{- 1}{\frac{c_{2} - c_{1}}{1 + c_{2}c_{1}} + an^{- 1}\frac{c_{3} - c_{2}}{1 + c_{3}c_{2}}}} + ... + an^{- 1}\frac{1}{c_{n}}$ is equal to

Question

$	an^{- 1}{\frac{c_{1}x - y}{c_{1}y + x} + 	an^{- 1}{\frac{c_{2} - c_{1}}{1 + c_{2}c_{1}} + 	an^{- 1}\frac{c_{3} - c_{2}}{1 + c_{3}c_{2}}}} + ... + 	an^{- 1}\frac{1}{c_{n}}$ is equal to

Dr. Abubacker · Accepted Answer

(c)
$	an^{- 1}{\left( \frac{c_{1} - y}{c_{1}y + x} ight) + 	an^{- 1}{\left( \frac{c_{2} - c_{1}}{1 + c_{2}c_{1}} ight) + 	an^{- 1}{\left( \frac{c_{3} - c_{2}}{1 + c_{3}c_{2}} ight) + ... + 	an^{- 1}\frac{1}{c_{n}}}}}$
$= 	an^{- 1}{\left( \frac{\frac{x}{y} - \frac{1}{c_{1}}}{1 + \frac{x}{y} \bullet \frac{1}{c_{1}}} ight) + 	an^{- 1}{\left( \frac{\frac{1}{c_{1}} - \frac{1}{c_{2}}}{1 + \frac{1}{c_{1}c_{2}}} ight) + 	an^{- 1}{\left( \frac{\frac{1}{c_{2}} - \frac{1}{c_{3}}}{1 + \frac{1}{c_{2}c_{3}}} ight) + ... + 	an^{- 1}\frac{1}{c_{n}}}}}$
$= 	an^{- 1}{\ \frac{x}{y} - 	an^{- 1}{\ \frac{1}{c_{1}} + 	an^{- 1}{\ \frac{1}{c_{1}} - 	an^{- 1}{\ \frac{1}{c_{2}} + 	an^{- 1}{\ \frac{1}{c\_ 2}}}}}}$
$- 	an^{- 1}\frac{1}{c_{3}} + ... + 	an^{- 1}{\frac{1}{c_{n - 1}} - 	an^{- 1}{\frac{1}{c_{n}} + 	an^{- 1}\frac{1}{c_{n}}}}$
$= 	an^{- 1}\left( \frac{x}{y} ight)$

Q. $\tan^{- 1}{\frac{c_{1}x - y}{c_{1}y + x} + \tan^{- 1}{\frac{c_{2} - c_{1}}{1 + c_{2}c_{1}} + \tan^{- 1}\frac{c_{3} - c_{2}}{1 + c_{3}c_{2}}}} + ... + \tan^{- 1}\frac{1}{c_{n}}$ is equal to

Explanation

Reviewed by Dr. Abubacker

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