First slide

Multiple and sub- multiple Angles

Question

If $\sin β$ is geometric mean between $\sin α$ and $\cos α,$ then $\cos 2 β =$

Moderate

A

$2 \sin^{2} (\frac{π}{4} - α) o r 2 \cos^{2} (\frac{π}{4} + α)$
B

$2 \sin^{2} (\frac{π}{3} - α) o r 2 \cos^{2} (\frac{π}{3} + α)$
C

$\sin^{2} (\frac{π}{4} - α) o r \cos^{2} (\frac{π}{4} + α)$
D

$\sin^{2} (\frac{π}{3} - α) o r \cos^{2} (\frac{π}{3} + α)$

Solution

$\sin^{2} β = \sin α \cos α,$
$\cos 2 β = 1 - 2 \sin α \cos α = {(\sin α - \cos α)}^{2}$

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