49/tg^2 (а+5п/2), если sina/2=1/3

[latex] \frac{49}{tg^2( \alpha + \frac{5 \pi }{2}) }[/latex],  если  [latex]sin \frac{ \alpha }{2} = \frac{1}{3} [/latex] [latex]sin \frac{ \alpha }{2} = \frac{1}{3}[/latex] [latex]sin^2 \frac{ \alpha }{2} = \frac{1}{9}[/latex] [latex]sin^2 \frac{ \alpha }{2} = \frac{1-cos \alpha }{2}[/latex] [latex] \frac{1-cos \alpha }{2}= \frac{1}{9} [/latex] [latex] {1-cos \alpha }= \frac{2}{9} [/latex] [latex] {cos \alpha }= 1- \frac{2}{9} [/latex] [latex] {cos \alpha }= \frac{7}{9} [/latex] [latex] {cos^2 \alpha }= \frac{49}{81} [/latex] [latex]sin^2 \alpha +cos^2 \alpha =1[/latex] [latex]sin^2 \alpha =1-cos^2 \alpha =1- \frac{49}{81} = \frac{32}{49} [/latex] [latex]ctg^2 \alpha = \frac{cos^2 \alpha }{sin^2 \alpha }= \frac{49}{81} : \frac{32}{81} = \frac{49}{81} * \frac{81}{32}= \frac{49}{32} [/latex] [latex] \frac{49}{tg^2( \alpha + \frac{5 \pi }{2}) }= \frac{49}{tg^2( \alpha + \frac{ \pi }{2}) }= \frac{49}{ctg^2\alpha }[/latex][latex]=49: \frac{49}{32}=49* \frac{32}{49}=32 [/latex] Ответ:  [latex]32[/latex]