49/tg^2 (а+5п/2), если sina/2=1/3

$\frac{49}{tg^2( \alpha + \frac{5 \pi }{2}) }$ , если $sin \frac{ \alpha }{2} = \frac{1}{3}$

$sin \frac{ \alpha }{2} = \frac{1}{3}$

$sin^2 \frac{ \alpha }{2} = \frac{1}{9}$

$sin^2 \frac{ \alpha }{2} = \frac{1-cos \alpha }{2}$

$\frac{1-cos \alpha }{2}= \frac{1}{9}$

${1-cos \alpha }= \frac{2}{9}$

${cos \alpha }= 1- \frac{2}{9}$

${cos \alpha }= \frac{7}{9}$

${cos^2 \alpha }= \frac{49}{81}$

$sin^2 \alpha +cos^2 \alpha =1$

$sin^2 \alpha =1-cos^2 \alpha =1- \frac{49}{81} = \frac{32}{49}$

$ctg^2 \alpha = \frac{cos^2 \alpha }{sin^2 \alpha }= \frac{49}{81} : \frac{32}{81} = \frac{49}{81} * \frac{81}{32}= \frac{49}{32}$

$\frac{49}{tg^2( \alpha + \frac{5 \pi }{2}) }= \frac{49}{tg^2( \alpha + \frac{ \pi }{2}) }= \frac{49}{ctg^2\alpha }$ $=49: \frac{49}{32}=49* \frac{32}{49}=32$

Ответ: $32$