If $1 + \sin x + {\sin ^2}x + ...{\rm{upto}}\;\infty = 4 + 2\sqrt 3 ,0 < x < \pi \;{\rm{and}}\;x \ne \frac{\pi }{2}$, then $x$ is equal to

$\frac{\pi }{3},\frac{{5\pi }}{6}$

$\frac{{2\pi }}{3},\frac{\pi }{6}$

$\frac{\pi }{6},\frac{\pi }{3}$

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

1 of 1

Application +4 | -1

1 + \sin x + {\sin ^2}x + ...\mathrm{upto}\;\infty = 4 + 2\sqrt 3 ,0 < x < \pi \;\mathrm{and}\;x \ne \frac{\pi }{2}

, then

x

is equal to

View answer and explanation

Correct option: C

\frac{\pi }{3},\frac{{2\pi }}{3}

Option C (

\frac{\pi }{3},\frac{{2\pi }}{3}

) is correct because solving the infinite geometric series and then finding the sine inverse gives these two solutions within the specified range.

Practice All Chapter MCQs →

A=\{1,2,3\}, B=\{3,4\}, C=\{4,5,6\}

{A} \cup({B} \cap {C})

A-(B \cap C)

(B \cup C)-A

a,b,c

a,x,b

b,y,c

{x^2},{b^2},{y^2}

P(x)=1-x+x^2-x^3+\ldots+x^{2012}

y

Q(y)=a_0+a_1 y+\ldots+a_{2012} y^{2012}

y=x-2

\sum\limits_{{i=0}}^{2012} a_i

\log \left(\frac{5 c}{a}\right), \log \left(\frac{3 b}{5 c}\right)

\log \left(\frac{a}{3 b}\right)

A P

a, b

G P

a, b, c

\frac{3}{4}