Question

Sqrt tga + sqrt ctga, если tga+ctga=a(a>0)

Answer 1

Tga+ctga=sina/cosa+cosa/sina=(sina^2+cosa^2)/sinacosa=1/sinacosa=a
sinacosa=1/a
$\sqrt{tga}+ \sqrt{ctga}= \sqrt{sina/cosa}+ \sqrt{cosa/sina} =(sina+cosa)/ \sqrt{sinacosa}=a/ \sqrt{1/a} = a/a^{-1/2}=a^{3/2}$