JEE 2023 — Mathematics PYQ

1. First term: $\frac{1+\sqrt{3}}{3+\sqrt{3}}$ ko simplify karne ke liye niche se $\sqrt{3}$ common lein: $\frac{1+\sqrt{3}}{\sqrt{3}(\sqrt{3}+1)}=\frac{1}{\sqrt{3}}$. Iska ${\tan }^{-1}$ hota hai $\frac{\pi }{6}$.

2. Second term: Root ke andar simplification karein: $\frac{4(2+\sqrt{3})}{3(2+\sqrt{3})}=\frac{4}{3}$. Phir ${\sec }^{-1}\left(\sqrt{\frac{4}{3}}\right)={\sec }^{-1}\left(\frac{2}{\sqrt{3}}\right)$, jo ki hota hai $\frac{\pi }{6}$.

3. Final Result: $\frac{\pi }{6}+\frac{\pi }{6}=\frac{\pi }{3}$.

Isliye sahi option (A) hai.