求证：tan²α-sin²α=tan²α*sin²α

网友回答

证明：tan²α-sin²α
=sin²α/cos²α-sin²α
=(sin²α-sin²αcos²α)/cos²α
=sin²α(1-cos²α)/cos²α
=sin²α*sin²α/cos²α
=tan²α*sin²α
所以tan²α-sin²α=tan²α*sin²α
======以下答案可供参考======
供参考答案1:
tan²α-sin²α
=sin²α/cos²α-sin²α
=(sinα)^2. [1-(cosα)^2]/(cosα)^2
=(sinα)^2 . (sinα)^2/(cosα)^2
=(sinα)^2.(tanα)^2