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Sin2A and Cos2A in Terms of tanA

If 2 sec 2 α=...

Question

If $2 s e c 2 α = t a n β + c o t β$ , then one positive value of $α + β$ is

A

$\frac{π}{2}$

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B

$\frac{π}{4}$

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C

$\frac{π}{3}$

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D

$0$

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Solution

The correct option is B
$\frac{π}{4}$

$2 s e c 2 α = (\frac{1}{s i n β c o s β})$

$\Rightarrow 2 α = \frac{π}{2} - 2 β \Rightarrow α + β = \frac{π}{4}$

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