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

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 3. trignometrical ratios,functions and identities1 Mark
MCQ
If $\alpha$ lies in the second quadrant,then $\sqrt {\frac{{1 - \sin \alpha }}{{1 + \sin \alpha }}}  - \sqrt {\frac{{1 + \sin \alpha }}{{1 - \sin \alpha }}}  =$
  • A
    $tan\,\,\alpha$
  • ✓
    $2\,\, tan\,\,\alpha$
  • C
    $2\,\, cot\,\,\alpha$
  • D
    $cot\,\,\alpha$
✓

Answer

Correct option: B.
$2\,\, tan\,\,\alpha$
b
Given expression

${=\frac{(1-\sin \alpha)-(1+\sin \alpha)}{\sqrt{1-\sin ^{2} \alpha}}} $

${=\frac{-2 \sin \alpha}{|\cos \alpha|}=\frac{-2 \sin \alpha}{-\cos \alpha}} $

$  \left[\because {\frac{\pi }{2} < \alpha  < \pi \therefore \cos \alpha {\rm{ is  - ve }}} \right] = 2{\rm{tan}}\alpha $

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