Question

49/tg^2 (а+5п/2), если sina/2=1/3

Answer 1

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

Ответ:  $32$