The value of \(\tan^{-1}\displaystyle\frac{2}{11}+\tan^{-1}\displaystyle\frac{7}{24}\) is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\tan^{-1}\displaystyle\frac{1}{2}\)
For ab < 1, the sum formula is \(\tan^{-1}a+\tan^{-1}b = \tan^{-1}\frac{a+b}{1-ab}\). Here ab = 14/264 < 1.
\( \displaystyle a+b = \frac{2}{11}+\frac{7}{24} = \frac{48+77}{264} = \frac{125}{264} \)
\( \displaystyle 1-ab = 1-\frac{14}{264} = \frac{250}{264} \)
\( \displaystyle \frac{a+b}{1-ab} = \frac{125}{250} = \frac{1}{2} \)
So the value is \(\tan^{-1}\frac{1}{2}\).
Note: This topic was not in the CUET 2026 syllabus.