$1 + \sin \,\,x + {\sin ^2}x + \ldots $ to $\infty = 4 + 2\,\sqrt 3 $, if

$x = \frac{{2\pi }}{3}\,\,\;{\rm{or,}}\,\,\frac{\pi }{3}$

JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

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Application +4 | -1

1 + \sin \,\,x + {\sin ^2}x + \ldots

\infty = 4 + 2\,\sqrt 3

, if

View answer and explanation

Correct option: A

x = \frac{{2\pi }}{3}\,\,\;\mathrm{or,}\,\,\frac{\pi }{3}

Option A (

x = \frac{{2\pi }}{{3}}\,\,\;\mathrm{or}\,\,\frac{\pi }{3}

) is correct because it satisfies the given infinite geometric series equation after solving for sin(x).

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