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

题目

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

答案

(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.