First slide

Multiple and sub- multiple Angles

Question

If $\cos (θ - α), \cos θ, \cos (θ + α)$ are in H.P. then $\cos θ . \sec \frac{α}{2} =$

Moderate

A

$- \sqrt{2}$
B

$\sqrt{2}$
C

$\pm \sqrt{2}$
D

1

Solution

Apply H.P. condition
$\frac{2}{\cos θ} = \frac{1}{\cos (θ - α)} + \frac{1}{\cos (θ + α)} \Rightarrow \frac{2}{\cos θ} = \frac{2 \cos θ \cos α}{\cos^{2} θ - \sin^{2} α}$

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