Question

निम्नलिखित को सिद्ध कीजिए:

${\displaystyle {\text{tan}}^{-1} \frac{2}{11}+{\text{tan}}^{-1}\frac{7}{24}={\text{tan}}^{-1}\frac{1}{2}}$

Answer 1

${\displaystyle {\text{tan}}^{-1} \frac{2}{11}+{\text{tan}}^{-1}\frac{7}{24}={\text{tan}}^{-1}\frac{1}{2}}$

${\displaystyle \Rightarrow {\text{tan}}^{-1}\frac{2}{11}+{\text{tan}}^{-1}\frac{7}{24}}$

${\displaystyle \Rightarrow {\text{tan}}^{-1}\frac{\frac{2}{11}+\frac{7}{24}}{1-\frac{2}{11}\times \frac{7}{24}}}$

${\displaystyle {\Rightarrow }^{-1}\frac{\frac{48+77}{11\times 24}}{\frac{11\times 24-14}{11\times 24}}}$

${\displaystyle \Rightarrow {\text{tan}}^{-1}\frac{48+77}{264-14}}$

${\displaystyle ={\text{tan}}^{-1}\frac{125}{250}}$

${\displaystyle ={\text{tan}}^{-1}\frac{1}{2}}$