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  • Find the value of <img alt="2\tan^{-1}\frac{5}{12}-\tan^{-1}\frac{1}{70}+\tan^{-1}\frac{1}{99}" src="http://entrancecorner.oncodecogs.com/gif.latex?2%5Ctan%5E%7B-1%7D%5Cfrac%7B5%7D%7B12%7D-%5C

Find the value of 2\tan^{-1}\frac{5}{12}-\tan^{-1}\frac{1}{70}+\tan^{-1}\frac{1}{99}

Option: 1

1


Option: 2

\frac{\pi}{4}


Option: 3

\frac{-\pi}{4}


Option: 4

\frac{3\pi}{4}


Answers (1)

best_answer

\\2\tan^{-1}\frac{5}{12}-\tan^{-1}\frac{1}{70}+\tan^{-1}\frac{1}{99}\\=\tan^{-1}\frac{2\times\frac{5}{12}}{1-(\frac{5}{12})^2}- \{ \tan^{-1}\frac{1}{70}-\tan^{-1}\frac{1}{99} \}\\ =\tan^{-1}\frac{120}{119}-\tan^{-1}(\frac{\frac{1}{70}-\frac{1}{99}}{1+\frac{1}{70}\times \frac{1}{99}})\\ =\tan^{-1}\frac{120}{119}-\tan^{-1}(\frac{29}{6931})\\ =\tan^{-1}\frac{120}{119}-\tan^{-1}(\frac{1}{239})\\ =\tan^{-1}(\frac{\frac{120}{119}-\frac{1}{239}}{1+\frac{120}{119}\times \frac{1}{239}})\\ =\tan^{-1}( 1)\\ =\frac{\pi}{4}

Posted by

Deependra Verma

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