If cos⁡α+cos⁡β=0=sin⁡α+sin⁡β then cos⁡2α+cos⁡2β is equal to

# If $\mathrm{cos}\mathrm{\alpha }+\mathrm{cos}\mathrm{\beta }=0=\mathrm{sin}\mathrm{\alpha }+\mathrm{sin}\mathrm{\beta }$ then $\mathrm{cos}2\mathrm{\alpha }+\mathrm{cos}2\mathrm{\beta }$ is equal to

1. A

$2\mathrm{cos}\left(\mathrm{\alpha }+\mathrm{\beta }\right)$

2. B

$-2\mathrm{cos}\left(\mathrm{\alpha }+\mathrm{\beta }\right)$

3. C

$3\mathrm{cos}\left(\mathrm{\alpha }+\mathrm{\beta }\right)$

4. D

None of these

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### Solution:

Given

On squaring and subtracting both the equations, we get

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