Write the value of tan(2tan-10/5)
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Posted by Shubham Verma 6 years, 3 months ago
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Sia ? 6 years, 3 months ago
The given inverse trigonometric function is
tan {tex}\left[ 2 \tan ^ { - 1 } (\frac { 1 } { 5 } )\right]{/tex}
Now, {tex}\tan \left( 2 \tan ^ { - 1 } \frac { 1 } { 5 } \right) = \tan \left[ \tan ^ { - 1 } \left( \frac { 2 \times \frac { 1 } { 5 } } { 1 - \left( \frac { 1 } { 5 } \right) ^ { 2 } } \right) \right]{/tex}
{tex}\left[ \because 2 \tan ^ { - 1 } x = \tan ^ { - 1 } \left( \frac { 2 x } { 1 - x ^ { 2 } } \right) ; - 1 < x < 1 \right]{/tex}
{tex}= \tan \left[ \tan ^ { - 1 } \left( \frac { 2 \times 5 } { 24 } \right) \right] = \tan \left[ \tan ^ { - 1 } \left( \frac { 5 } { 12 } \right) \right] = \frac { 5 } { 12 }{/tex}
{tex}\left[ \because \tan \left( \tan ^ { - 1 } x \right) = x ; \forall x \in R \right]{/tex}
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