If 2sec 2alpha = tan beta + cot beta , then o | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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 $ 

==> $2\alpha + 2\beta = \frac{\pi }{2}$ 

==> $\alpha + \beta = \frac{\pi }{4}$.

If $2\sec 2\alpha = \tan \beta + \cot \beta ,$ then one of the values of $\alpha + \beta $ is

Similar Questions

Let $S=\left\{x \in(-\pi, \pi): x \neq 0, \pm \frac{\pi}{2}\right\}$. The sum of all distinct solutions of the equation $\sqrt{3} \sec x+\operatorname{cosec} x+2(\tan x-\cot x)=0$ in the set $S$ is equal to

$\frac{{\sin 3A - \cos \left( {\frac{\pi }{2} - A} \right)}}{{\cos A + \cos (\pi + 3A)}} = $

Prove that: $\cos 4 x=1-8 \sin ^{2} x \cos ^{2} x$

$cosec^2\theta $ = $\frac{4xy}{(x +y)^2}$ is true if and only if

$1 - 2{\sin ^2}\left( {\frac{\pi }{4} + \theta } \right) = $