First slide

Multiple and sub- multiple Angles

Question

If $\cos α + \cos β = \sin α + \sin β$ ,then $\cos 2 α + \cos 2 β =$

Easy

A

$- 2 \sin (α + β)$
B

$- 2 \cos (α + β)$
C

$2 \sin (α + β)$
D

$2 \cos (α + β)$

Solution

$\begin{array}{l} \cos α + \cos β = \sin α + \sin β \\ o n S q u a r i n g, \cos^{2} α + \cos^{2} β + 2 \cos α \cos β = \sin^{2} α + \sin^{2} β + 2 \sin α \sin β \\ \Rightarrow \cos^{2} α - \sin^{2} α + \cos^{2} β - \sin^{2} β = - 2 (\cos α \cos β - \sin α \sin β) \\ \Rightarrow \cos 2 α + \cos 2 β = - 2 \cos (α + β) \end{array}$

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