Question

Упростите выражение:  
$frac{sin ^{2} alpha -tg ^{2} alpha }{cos^{2} alpha -ctg ^{2} alpha }$

Answer 1

sin²a -tg²a=sin²a - sin²a/cos²a=(sin²acos²a - sin²a)/cos²a=sin²a(cos²a-1)/cos²a=
=-sin^4a/cos²a
cos²a - ctg²a=cos²a - cos²a/sin²a=(cos²asin²a - cos²a)/sin²a=cos²a(sin²a-1)/sin²a=
=-cos^4a/sin²a
(sin²a -tg²a)/(cos²a - ctg²a)=-sin^4a/cos²a : -cos^4a/sin²a=sin^4a/cos²a * sin²a/cos^4a=
=sin^6a/cos^6a=tg^6a

Answer 2

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