Number of solutions of equation secx = 1 + cosx + cos^2x + ........ ∞ in x ∈ [-50 π, 50 π] is

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Trigonometrical Equations

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Number of solutions of equation $secx = 1 + cosx + cos^2x + ........ \infty$ in $x \in [-50 \pi, 50 \pi]$ is -

A

$96$

B

$99$

C

$100$

D

$101$

Solution

$\sec x=\frac{1}{1-\cos x} \Rightarrow \cos x=1-\cos x$

$\Rightarrow \cos x=\frac{1}{2}$

2 solutions in $[0,2 \pi]$

$\therefore 100$ solutions.

Standard 11

Mathematics

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