(a) दिये गये समीकरण को निम्न प्रकार लिखा जा सकता है

$\frac{2}{{\cos 2\alpha }} = \frac{{\sin \beta }}{{\cos \beta }} + \frac{{\cos \beta }}{{\sin \beta }}$

$= \frac{{{{\sin }^2}\beta + {{\cos }^2}\beta }}{{\cos \beta \sin \beta }}$

$ = \frac{1}{{\cos \beta .\sin \beta }}$ 

==> $\cos 2\alpha = \sin 2\beta $ 

==> $\cos 2\alpha $= $\cos \,\left( {\frac{\pi }{2} – 2\beta } \right)$

==> $2\alpha = \frac{\pi }{2} – 2\beta $ 

==> $2\alpha + 2\beta = \frac{\pi }{2}$ 

==> $\alpha + \beta = \frac{\pi }{4}$.