If 1 + cos α + {cos ^2}α + .......,∞ = 2 - √ {2,} then α , (0 < α < π ) is

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8. Sequences and Series

easy

If $1 + \cos \alpha + {\cos ^2}\alpha + .......\,\infty = 2 - \sqrt {2,} $ then $\alpha ,$ $(0 < \alpha < \pi )$ is

A

$\pi /8$

B

$\pi /6$

C

$\pi /4$

D

$3\pi /4$

Solution

(d) $1 – \cos \alpha = \frac{1}{{2 – \sqrt 2 }} = 1 + \frac{1}{{\sqrt 2 }}$

==> $\cos \alpha = – \frac{1}{{\sqrt 2 }} = \cos \frac{{3\pi }}{4}$

==> $\alpha = \frac{{3\pi }}{4}$.

Standard 11

Mathematics

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