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[tex]sin \frac{pi}{12} *cos \frac{11pi}{12} + \frac{tg \frac{pi}{8} }{2-2 tg^{2} \frac{pi}{8} } =?[/tex]

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DariosI

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$\frac{1}{2} (2sin \frac{ \pi }{12}*cos \frac{ \pi }{12})+ \frac{tg \frac{ \pi }{8} }{2( 1-tg ^{2} \frac{ \pi }{12} ) } = \frac{1}{2} sin \frac{ \pi }{6}+ \frac{tg \frac{ \pi }{8} }{2( \frac{cos ^{2} \frac{ \pi }{8}-sin ^{2} \frac{ \pi }{8} }{cos ^{2} \frac{ \pi }{8} } ) } =$ $\frac{1}{2} * \frac{1}{2} + \frac{tg \frac{ \pi }{8} *cos ^{2} \frac{ \pi }{8}}{2( cos \frac{ \pi }{4} ) } =\frac{1}{4} + \frac{sin \frac{ \pi }{8} *cos \frac{ \pi }{8}}{2( cos \frac{ \pi }{4} ) }=\frac{1}{4} + \frac{sin \frac{ \pi }{4} }{4 cos \frac{ \pi }{4} }=$ $\frac{1}{4} + \frac{1}{4}*tg \frac{ \pi }{4} =\frac{1}{4} + \frac{1}{4}= \frac{1}{2}$

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