If $\alpha$ and $\beta$ satisfying $2\sec{2\alpha = an{\beta + \cot\beta}}$, then $\alpha + \beta$ is equal to

Question

If $\alpha$ and $\beta$ satisfying $2\sec{2\alpha = 	an{\beta + \cot\beta}}$, then $\alpha + \beta$ is equal to

Dr. Abubacker · Accepted Answer

(c)
Given, $2\sec{2\alpha =}	an\beta + \cot\beta$
$\Rightarrow \ \ 2\sec{2\alpha = \frac{\sin^{2}\beta + \cos^{2}\beta}{\sin{\beta\cos\beta}}}$
$\Rightarrow \ \ \frac{2}{\cos{2\alpha}} = \frac{1}{\sin\beta\cos\beta}$
$\Rightarrow \ \sin{2\beta = \cos{2\alpha}}$
$\Rightarrow \ \ \alpha + \beta = \frac{\pi}{4}$

Q. If $\alpha$ and $\beta$ satisfying $2\sec{2\alpha = \tan{\beta + \cot\beta}}$, then $\alpha + \beta$ is equal to

Explanation

Reviewed by Dr. Abubacker

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