(tan＾2α－cot＾2α)/(sin＾2α－cos＾2α)＝sec＾2α•csc＾2α

(tan＾2α－cot＾2α)/(sin＾2α－cos＾2α)＝sec＾2α•csc＾2α
(tan＾2α－cot＾2α)/(sin＾2α－cos＾2α)＝sec＾2α•csc＾2α

(tan＾2α－cot＾2α)/(sin＾2α－cos＾2α)＝sec＾2α•csc＾2α
(tan²α-cot²α)/(sin²α-cos²α)
=(sin²α/cos²α-cos²α/sin²α)/(sin²α-cos²α)
=(sin⁴α-cos⁴α)/[sin²αcos²α(sin²α-cos²α)] 这一步是分子分母同乘以sin²αcos²α
=(sin²α+cos²α)(sin²α-cos²α)/[sin²αcos²α(sin²α-cos²α)] 注意sin²α+cos²α=1
=1/(sin²αcos²α)
=sec²αcsc²α,等式成立.

？，恒等式；
等号左端=[(sin²α/cos²α)-(cos²α/sin²α)] /(sin²α-cos²α)
=[(sin²αsin²α-cos²αcos²α]/[(sin²α-cos²α)(sin²α•cos²α)]
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？，恒等式；
等号左端=[(sin²α/cos²α)-(cos²α/sin²α)] /(sin²α-cos²α)
=[(sin²αsin²α-cos²αcos²α]/[(sin²α-cos²α)(sin²α•cos²α)]
=[(sin²α-cos²α)(sin²α+cos²)]/[(sin²α-cos²α)(sin²αcos²α)]
=1/(sin²αcos²α)=sec²α•csc²α=等式右端；

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