Question

Упростите выражение

$frac{cos ^{2} alpha }{1+tg ^{2} alpha } - frac{sin ^{2} alpha }{1+ctg ^{2} alpha }$

Answer 1

cos²a:(1+sin²a/cos²a)-sin²a:(1+cos²a/sin²a)=
=cos²a*cos²a/(cos²a+sin²a)-sin²a*sin²a/(sin²a+cos²a)=cos^4a-sin^4a=
=(cos²a-sin²a)(cos²a+sin²a)=cos2a