Question

Упростить выражение:

ctga/(tga+ctga) +sin^2(П-а)

Answer 1

$tga+ctga=frac{sina}{cosa}+frac{cosa}{sina}=frac{sin^2a+cos^2a}{cosa*sina}=frac{1}{cosa*sina}$
$(sin(pi-a))^2=(sina)^2=sin^2a$

$frac{frac{cosa}{sina}}{frac{1}{sina*cosa}}+sin^2a=frac{cosa*sina*cosa}{sina}+sin^2a=cos^2a+sin^2a=1$

Answer 2

cosa/sina*(sina/cosa +cosa/sina) +sin²a=cosa/sina*(sin²a+cos²a)/sinacosa +sin²a=
=1/sin² +sin²a=1+ctg²a +sin²a