Question

The value of $$\tan ({\cos }^{-1}\frac{3}{5}+{\tan }^{-1}\frac{1}{4})$$

 

विकल्प

• ${\displaystyle \frac{19}{8}}$

• ${\displaystyle \frac{8}{19}}$

• ${\displaystyle \frac{19}{12}}$

• ${\displaystyle \frac{3}{4}}$

Answer 1

$$\tan ({\cos }^{-1}\frac{3}{5}+{\tan }^{-1}\frac{1}{4})=\tan ({\tan }^{-1}\frac{\sqrt{1-\frac{9}{25}}}{\frac{3}{5}}+{\tan }^{-1}\frac{1}{4})$$
$$=\tan ({\tan }^{-1}\frac{\frac{4}{5}}{\frac{3}{5}}+{\tan }^{-1}\frac{1}{4})$$
$$=\tan ({\tan }^{-1}\frac{4}{3}+{\tan }^{-1}\frac{1}{4})$$
$$=\tan ({\tan }^{-1}\frac{\frac{4}{3}+\frac{1}{4}}{1-\frac{1}{3}})$$
$$=\frac{\frac{16+3}{12}}{\frac{2}{3}}$$
$$=\frac{19}{8}$$

Hence, the correct answer is option (a).