Question

найдите ctg^2(п/2 + альфа) если sin a = корень 21/5

Answer 1

$Ctg ^{2} ( frac{ pi }{2}+ alpha )=tg ^{2} alpha \\1+tg ^{2} alpha = frac{1}{Cos ^{2} alpha }\\tg ^{2} alpha = frac{1}{Cos ^{2} alpha } -1\\Cos ^{2} alpha =1-Sin ^{2} alpha =1-( frac{ sqrt{21} }{5} ) ^{2}=1- frac{21}{25} = frac{4}{25} \\tg ^{2} alpha = frac{1}{ frac{4}{25} } -1= frac{25}{4} -1= frac{21}{25}=0,84$