【数学】高一三角函数证明题

题目

【数学】高一三角函数证明题
求证：tan^2α-sin^2α=tan^α*sin^2α

答案

tan^2α-sin^2α
=sin^2a/cos^2a-sin^2a
=sin^2a(1/cos^2a-1)
=sin^2a {(1-cos^2a)/cos^2a}
=sin^2a {sin^2a/cos^2a}
=sin^2a * tan^2a
记住tana=sina/cosa