If $1\, + \,\sin x\, + \,{\sin ^2}x\, + \,...\infty \, = \,4\, + \,2\sqrt 3 ,\,0\, < \,x\, < \,\pi $ then
If $1\, + \,\sin x\, + \,{\sin ^2}x\, + \,...\infty \, = \,4\, + \,2\sqrt 3 ,\,0\, < \,x\, < \,\pi $ then
- A
$x = \frac{\pi }{6}$
- B
$x = \frac{\pi }{3}$
- C
$x = \frac{\pi }{6}$ or $\frac{\pi }{3}$
- D
none of these
Similar Questions
The sum to infinity of the following series $2 + \frac{1}{2} + \frac{1}{3} + \frac{1}{{{2^2}}} + \frac{1}{{{3^2}}} + \frac{1}{{{2^3}}} + \frac{1}{{{3^3}}} + ........$, will be
The sum to infinity of the following series $2 + \frac{1}{2} + \frac{1}{3} + \frac{1}{{{2^2}}} + \frac{1}{{{3^2}}} + \frac{1}{{{2^3}}} + \frac{1}{{{3^3}}} + ........$, will be
If $a,\;b,\;c$ are in $A.P.$, then ${3^a},\;{3^b},\;{3^c}$ shall be in
If $a,\;b,\;c$ are in $A.P.$, then ${3^a},\;{3^b},\;{3^c}$ shall be in
Given a $G.P.$ with $a=729$ and $7^{\text {th }}$ term $64,$ determine $S_{7}$
Given a $G.P.$ with $a=729$ and $7^{\text {th }}$ term $64,$ determine $S_{7}$
If $x$ is added to each of numbers $3, 9, 21$ so that the resulting numbers may be in $G.P.$, then the value of $x$ will be
If $x$ is added to each of numbers $3, 9, 21$ so that the resulting numbers may be in $G.P.$, then the value of $x$ will be
If the sum of the second, third and fourth terms of a positive term $G.P.$ is $3$ and the sum of its sixth, seventh and eighth terms is $243,$ then the sum of the first $50$ terms of this $G.P.$ is
If the sum of the second, third and fourth terms of a positive term $G.P.$ is $3$ and the sum of its sixth, seventh and eighth terms is $243,$ then the sum of the first $50$ terms of this $G.P.$ is
- [JEE MAIN 2020]