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3. trignometrical ratios,functions and identities — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS3. trignometrical ratios,functions and identities1 Mark
MCQ
If $cos\, \alpha = \frac{{2\,\cos \,\beta \,\, - \,\,1}}{{2\,\, - \,\,\cos \,\beta }}$ then $tan \frac{\alpha}{2}$ $cot \frac{\beta}{2}$ has the value equal to, where $(0 < \alpha < \pi$ and $0 < \beta < \pi$)
  • A
    $2$
  • B
    $\sqrt 2 \,$
  • C
    $3$
  • ✓
    $\sqrt 3 \,$
✓

Answer

Correct option: D.
$\sqrt 3 \,$
d
$\frac{1}{{\cos \,\alpha }} = \frac{{2\,\, - \,\,\cos \,\beta }}{{2\,\cos \,\beta \,\, - \,\,1}}$

Applying $C/D$

$ \Rightarrow = \frac{{1\,\, - \,\,\cos \,\alpha }}{{1\,\, + \,\,\cos \,\alpha }} = \frac{{3\,\left( {1\,\, - \,\,\cos \,\beta } \right)}}{{1\,\, + \,\,\cos \,\beta }}$

$\Rightarrow\, tan^2 \frac{\alpha}{2} = 3 tan^2 \frac{\beta}{2} \Rightarrow tan^2 \frac{\alpha}{2} \,cot^2 \frac{\beta}{2}= 3$

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