A) \[\frac{3+\sqrt{5}}{2}\]
B) \[3+\sqrt{5}\]
C) \[\frac{1}{2}(3-\sqrt{5})\]
D) None of these
Correct Answer: C
Solution :
Let\[{{\cos }^{-1}}\left( \frac{\sqrt{5}}{3} \right)=\alpha \], then\[\cos \alpha =\frac{\sqrt{5}}{3}\], where \[0<\alpha <\frac{\pi }{2}\] Now,\[\tan \frac{\alpha }{2}=\sqrt{\frac{1-\cos \alpha }{1+\cos \alpha }}=\sqrt{\frac{1-\sqrt{5}/3}{1+\sqrt{5}/3}}\] \[=\sqrt{\frac{3-\sqrt{5}}{3+\sqrt{5}}}=\sqrt{\frac{{{(3-\sqrt{5})}^{2}}}{9-5}}=\frac{1}{2}(3-\sqrt{5})\]
You need to login to perform this action.
You will be redirected in
3 sec
