Question

Докажите тождество: 1+tg^2a/1+ctg^2a=tg^2a

Answer 1

( 1+tg²α)/(1+ctg²α) = tg²α

( 1+tg²α)/(1+ctg²α) =

= ( 1 + (sin²α/cos²α)) / ( 1 + (cos²α/sin²α)) =

=  ( (cos²α+sin²α) /cos²α)) / ( (sin²α + cos²α) /sin²α)) =

=  ( 1 /cos²α)) / ( 1 /sin²α)) = ( 1 /cos²α)) / ( sin²α) = sin²α/cos²α = tg²α