MCQ
જો $2\sec 2\alpha = \tan \beta + \cot \beta ,$ તો $\alpha + \beta =. . . .$
- ✓$\frac{\pi }{4}$
- B$\frac{\pi }{2}$
- C$\pi $
- D$2\pi $
$\frac{2}{{\cos 2\alpha }} = \frac{{\sin \beta }}{{\cos \beta }} + \frac{{\cos \beta }}{{\sin \beta }}$
$= \frac{{{{\sin }^2}\beta + {{\cos }^2}\beta }}{{\cos \beta \sin \beta }}$
$ = \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 $
==> $2\alpha + 2\beta = \frac{\pi }{2}$
==> $\alpha + \beta = \frac{\pi }{4}$.
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