Question

док-жите тож-ество
$frac{1-cos^2t}{1-sin^2t} +tgt*ctgt= frac{1}{cos^2t}$

Answer 1

$frac{1-cos^2t}{1-sin^2t} +tgt*ctgt= frac{1}{cos^2t}$
$frac{1-cos^2t}{1-sin^2t} +tgt*ctgt= frac{sin^2t}{cos^2t} +1=tg^2+1= frac{1}{cos^2t}$
$frac{1}{cos^2t} =frac{1}{cos^2t}$   тождество доказано 

Answer 2

$dfrac{1-cos^2t}{1-sin^2t}+tgt*ctgt=dfrac{1}{cos^2t}\dfrac{1-cos^2t}{1-sin^2t}+tgt*ctgt=dfrac{sin^2t}{cos^2t}+1=dfrac{sin^2t+cos^2t}{cos^2t}=dfrac{1}{cos^2t}$