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Write the value of tan(2tan^(-1)(1/5)) - Mathematics

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Write the value of `tan(2tan^(-1)(1/5))`

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Solution

`2tan^(-1)x=tan^(-1)(2x)/(1-x^2)`

`therefore 2 tan^(-1)(1/5)=tan^(-1)((2(1/5))/(1-(1/5)^2))=tan^(-1)(5/12)`

Thus `tan (2tan^(-1)(1/5))=tan(tan^(-1)(5/12))=5/12`

Concept: Inverse Trigonometric Functions (Simplification and Examples)
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