• question_answer If $2\sec 2\alpha =\tan \beta +\cot \beta ,$then one of the values of $\alpha +\beta$is [Karnataka CET 2000] A) $\frac{\pi }{4}$ B) $\frac{\pi }{2}$ C) $\pi$ D) $2\pi$

The given equation may be written as $\frac{2}{\cos 2\alpha }=\frac{\sin \beta }{\cos \beta }+\frac{\cos \beta }{\sin \beta }=\frac{{{\sin }^{2}}\beta +{{\cos }^{2}}\beta }{\cos \beta \sin \beta }$$=\frac{1}{\cos \beta .\sin \beta }$ Þ $\cos 2\alpha =\sin 2\beta$ Þ $\cos 2\alpha$= $\cos \,\left( \frac{\pi }{2}-2\beta \right)$Þ $2\alpha =\frac{\pi }{2}-2\beta$  Þ  Þ .