求证1/sin²α+1/cos²α-cos²α/sin²α=2+tan²α.
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求证1/sin²α+1/cos²α-cos²α/sin²α=2+tan²α.
求证1/sin²α+1/cos²α-cos²α/sin²α=2+tan²α.
求证1/sin²α+1/cos²α-cos²α/sin²α=2+tan²α.
1/sin²α+1/cos²α-cos²α/sin²α
=(1-cos²α)/sin²α+1/cos²α
=sin²α/sin²α+1/cos²α
=1+(sin²α+cos²α)/cos²α
=1+tan²α+1
=2+tan²α
所以1/sin²α+1/cos²α-cos²α/sin²α=2+tan²α.