First slide

Multiple and sub- multiple Angles

Question

If $2 \sec 2 θ = \tan ϕ + \cot ϕ$ then one of the values of $θ + ϕ$ is

Easy

A

$\frac{π}{2}$
B

$\frac{π}{3}$
C

$\frac{π}{4}$
D

none of these

Solution

$\begin{array}{l} 2 \sec 2 θ = \tan ϕ + \cot ϕ \\ or \frac{2}{\cos 2 θ} = \frac{\sin^{2} ϕ + \cos^{2} ϕ}{\sin ϕcos ϕ} \\ or \frac{2}{\cos 2 θ} = \frac{1}{\sin ϕcos ϕ} \\ or \cos 2 θ = \sin 2 ϕ \\ or 2 θ = 90^{\circ} - 2 ϕ \\ or θ + ϕ = \frac{π}{4} \end{array}$

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