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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
$\sqrt 3 \,{\rm{cosec}}\,{20^o} - \sec \,{20^o} = $
  • A
    $2$
  • B
    $\frac{{2\,\sin {{20}^o}}}{{\sin {{40}^o}}}$
  • ✓
    $4$
  • D
    $\frac{{4\,\sin {{20}^o}}}{{\sin {{40}^o}}}$
✓

Answer

Correct option: C.
$4$
c
(c) $\sqrt 3 {\rm{cosec}}\,20^\circ - \sec 20^\circ = \frac{{\sqrt 3 }}{{\sin 20^\circ }} - \frac{1}{{\cos \,20^\circ }}$ 

$ = \frac{{\sqrt 3 \cos 20^\circ - \sin 20^\circ }}{{\sin 20^\circ \cos 20^\circ }} $

$= \frac{{2\left[ {\frac{{\sqrt 3 }}{2}\cos 20^\circ - \frac{1}{2}\sin \,20^\circ } \right]}}{{\frac{2}{2}\sin 20^\circ \cos 20^\circ }}$

$ = \frac{{4\cos (20^\circ + 30^\circ )}}{{\sin 40^\circ }} $

$= \frac{{4\cos 50^\circ }}{{\sin 40^\circ }} = \frac{{4\sin 40^\circ }}{{\sin 40^\circ }} = 4$.

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