MCQ
જો $\tan x + \tan \left( {\frac{\pi }{3} + x} \right) + \tan \left( {\frac{{2\pi }}{3} + x} \right) = 3,$ તો
- A$\tan x = 1$
- B$\tan 2x = 1$
- ✓$\tan 3x = 1$
- Dએકપણ નહિ.
$ = \tan x + \frac{{\tan x + \sqrt 3 }}{{1 - \sqrt 3 \,\tan x}} + \frac{{\tan x - \sqrt 3 }}{{1 + \sqrt 3 \,\tan x}}$
$ = \tan x + \frac{{8\tan x}}{{1 - 3{{\tan }^2}x}} $
$= \frac{{3\,(3\tan x - {{\tan }^3}x)}}{{1 - 3{{\tan }^2}x}} = 3\tan 3x$
Therefore, the given equation is
$\Rightarrow$ $3\tan 3x = 3$==> $\tan 3x = 1.$
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જ્યાં $x\, \in \,\,\left( {\frac{\pi }{2}\,,\,\frac{{3\pi }}{2}} \right)$
| ચલ $( x )$ | $x _{1}$ | $x _{1}$ | $x _{3} \ldots \ldots x _{15}$ |
| આવૃતિ $(f)$ | $f _{1}$ | $f _{1}$ | $f _{3} \ldots f _{15}$ |
જ્યાં $0< x _{1}< x _{2}< x _{3}<\ldots .< x _{15}=10$ અને $\sum \limits_{i=1}^{15} f_{i}>0,$ હોય તો પ્રમાણિત વિચલન ............ ના હોય શકે