The value of $\sec\left\lbrack an^{- 1}{\left( \frac{b + a}{b - a} ight) - an^{- 1}\left( \frac{a}{b} ight)} ight brack$ is

Question

The value of $\sec\left\lbrack 	an^{- 1}{\left( \frac{b + a}{b - a} ight) - 	an^{- 1}\left( \frac{a}{b} ight)} ightbrack$ is

Dr. Abubacker · Accepted Answer

(b)
$\sec\left\lbrack 	an^{- 1}{\left( \frac{b + a}{b - a} ight) - 	an^{- 1}\left( \frac{a}{b} ight)} ightbrack$
$\ \ \ \ \ \ \ \ \ \ \  = \sec\left\lbrack 	an^{- 1}\left\{ \frac{\frac{b + a}{b - a} - \frac{a}{b}}{1 + \left( \frac{b + a}{b - a} ight)\left( \frac{a}{b} ight)} ight\} ightbrack$
$\ \ \ \ \ \ \ \ \ \ \  = \sec{\lbrack	an^{- 1}{(1)}brack}$
$\ \ \ \ \ \ \ \ \ \ \  = \sec{\frac{\pi}{4} = \sqrt{2}}$

Q. The value of $\sec\left\lbrack \tan^{- 1}{\left( \frac{b + a}{b - a} \right) - \tan^{- 1}\left( \frac{a}{b} \right)} \right\rbrack$ is

Explanation

Reviewed by Dr. Abubacker

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