求证(2-cos²α)(2+tan²α)=(1+2tan²α)(2-sin²α)
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求证(2-cos²α)(2+tan²α)=(1+2tan²α)(2-sin²α)
求证(2-cos²α)(2+tan²α)=(1+2tan²α)(2-sin²α)
求证(2-cos²α)(2+tan²α)=(1+2tan²α)(2-sin²α)
左边=4+2(tana)^2-2(cosa)^2-(sina)^2
右边=2-(sina)^2+4(tana)^2-2(tanasina)^2,
左边-右边=2+2(tanasina)^2-2(tana)^2-2(cosa)^2
=2+2(tana)^2*[(sina)^2-1]-2(cosa)^2
=2-2(tanacosa)^2-2(cosa)^2
=2-2(sina)^2-2(cosa)^2
=0,
∴等式成立.