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CBSE Class 12 Math 2013 Solved Paper

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Question : 2 of 29
Marks: +1, -0
Write the value of tan (2tan⁡−115)\left(2\tan^{-1}\frac{1}{5}\right)
Solution:  
We know: 2 tan⁡−1x\tan^{-1}x = tan⁡−12x1−x2\tan^{-1}\frac{2x}{1-x^2}
⇒ 2tan⁡−1152\tan^{-1}\frac{1}{5} = tan⁡−12(15)1−(15)2\tan^{-1}\frac{2\left(\frac{1}{5}\right)}{1-\left(\frac{1}{5}\right)^2} = tan⁡−1252425\tan^{-1}\frac{\frac{2}{5}}{\frac{24}{25}} = tan⁡−1512\tan^{-1}\frac{5}{12}
∴ tan (2tan⁡−115)\left(2\tan^{-1}\frac{1}{5}\right) = tan (tan⁡−1512)\left(\tan^{-1}\frac{5}{12}\right) = 512\frac{5}{12}
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