2. inverse trigonometric function — ગણિત ધોરણ 12 સાયન્સ — Question

Put $\cos ^{-1}\left(\frac{\sqrt{5}}{3}\right)=\alpha$

$\quad \cos \alpha=\frac{\sqrt{5}}{3} \Rightarrow 0<\alpha<\frac{\pi}{2}$

$\tan \frac{\alpha}{2}=\sqrt{\frac{1-\cos \alpha}{1+\cos \alpha}}=\sqrt{\frac{1-\sqrt{5} / 3}{1+\sqrt{5} / 3}}$ 

$=\sqrt{\frac{3-\sqrt{5}}{3+\sqrt{5}}}=\sqrt{\frac{(3-\sqrt{5})^{2}}{9-5}}$

$=\frac{3-\sqrt{5}}{2}$