જો 2sec 2alpha = tan beta + cot beta , તો alp | vedclass

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Question

(a) The given equation may be written as

$\frac{2}{{\cos 2\alpha }} = \frac{{\sin \beta }}{{\cos \beta }} + \frac{{\cos \beta }}{{\sin \beta }}$

Vedclass · Accepted Answer

$\frac{\pi }{4}$

Vedclass · Answer

(a) 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 }}$ 

==> $\cos 2\alpha = \sin 2\beta $

==> $\cos 2\alpha $= $\cos \,\left( {\frac{\pi }{2} - 2\beta } \right)$

==> $2\alpha = \frac{\pi }{2} - 2\beta $

==> $2\alpha + 2\beta = \frac{\pi }{2}$

==> $\alpha + \beta = \frac{\pi }{4}$.

જો $2\sec 2\alpha = \tan \beta + \cot \beta ,$ તો $\alpha + \beta =. . . .$

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