First slide

Multiple and sub- multiple Angles

Question

If $2 | \sin 2 α | = | \tan β + \cot β |, α, β \in (\frac{π}{2}, π),$ then the value of $α + β$ is

Moderate

A

$\frac{3 π}{4}$
B

$π$
C

$\frac{3 π}{2}$
D

$\frac{5 π}{4}$

Solution

$\begin{array}{l} 2 | \sin 2 α | \leq 2 \\ and | \tan β + \cot β | = \frac{1}{| \sin βcos β |} = 2 | cosec 2 β | \geq 2 \\ ∴ 2 | \sin 2 α | = | \tan β + \cot β | = 2 \\ ∴ α = β = \frac{3 π}{4} \end{array}$

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