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Trigonometric Functions — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsTrigonometric Functions5 Marks
Question
If $\cos\alpha+\cos\beta=0=\sin\alpha+\sin\beta,$ then prove that $\cos2\alpha+\cos2\beta=-2\cos(\alpha+\beta).$
$\big[$Hint: $(\cos\alpha+\cos\beta)^2-(\sin\alpha+\sin\beta)^2=0\big]$
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Answer

Given that: $\cos\alpha+\cos\beta=0\ \dots\dots(\text{i})$
and $\sin\alpha+\sin\beta=0\ \dots\dots(\text{ii})$
From (i) and (ii) we have
$(\cos\alpha+\cos\beta)^2-(\sin\alpha+\sin\beta)^2=0$

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