MCQ
${\log _{\frac{1}{8}\cos e{c^2}\frac{\pi }{8}}}\,{\sin ^2}\frac{{3\pi }}{8}$ equals to
- A$0$
- B$\frac{1}{2}$
- ✓$1$
- Dnot defined
$ = {\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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