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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
${\log _{\frac{1}{8}\cos e{c^2}\frac{\pi }{8}}}\,{\sin ^2}\frac{{3\pi }}{8}$ equals to
  • A
    $0$
  • B
    $\frac{1}{2}$
  • ✓
    $1$
  • D
    not defined
✓

Answer

Correct option: C.
$1$
c
$E=\log _{\frac{1}{4\left(1-\cos \frac{\pi}{4}\right)}}\left(\frac{1-\cos \frac{3 \pi}{4}}{2}\right)$

$ = {\log _{\frac{1}{{4\left( {1 - \frac{1}{{\sqrt 2 }}} \right)}}}}\left( {\frac{{1 + \frac{1}{{\sqrt 2 }}}}{2}} \right) = {\log _{\frac{{\sqrt 2 }}{{4\sqrt 2  - 1}}}}\left( {\frac{{\sqrt 2  + 1}}{{2\sqrt 2 }}} \right)$

$=\log _{\frac{\sqrt{2}+1}{2 \sqrt{2}}}\left(\frac{\sqrt{2}+1}{2 \sqrt{2}}\right)=1$

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