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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
The value of $cosec \frac{\pi }{{18}} - \sqrt 3 \,sec\, \frac{\pi }{{18}}$ is a
  • A
    surd
  • B
    rational which is not integral
  • C
    negative natural number
  • ✓
    natural number
✓

Answer

Correct option: D.
natural number
d
$\frac{1}{{\sin \pi /18}}\,\, - \,\,\frac{{\sqrt 3 }}{{\cos \pi /18}}$ $=$$\frac{{2\,\left[ {\frac{1}{2}\cos \frac{\pi }{{18}}\, - \,\frac{{\sqrt 3 }}{2}\,\,\sin \frac{\pi }{{18}}} \right]}}{{\frac{{\sin \frac{\pi }{9}}}{2}}}$

$=$$\frac{{4\left[ {\sin \frac{\pi }{6}\,\,\cos \frac{\pi }{{18}}\,\, - \,\,\cos \frac{\pi }{6}\,\,\sin \frac{\pi }{{18}}} \right]}}{{\sin \frac{\pi }{9}}}$ $= 4$

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