已知sinα=1/9,求[cos(α-5π)tan(2π-α)/cos(3π/2 +α)]+tan²α 值

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已知sinα=1/9,求[cos(α-5π)tan(2π-α)/cos(3π/2 +α)]+tan²α 值

已知sinα=1/9,求[cos(α-5π)tan(2π-α)/cos(3π/2 +α)]+tan²α 值
已知sinα=1/9,求[cos(α-5π)tan(2π-α)/cos(3π/2 +α)]+tan²α 值

已知sinα=1/9,求[cos(α-5π)tan(2π-α)/cos(3π/2 +α)]+tan²α 值
sin²α+cos²α=1
所以cos²α=1-1/81=80/81
[cos(α-5π)tan(2π-α)/cos(3π/2 +α)]+tan²α
=[-cosα(-tanα)]/sinα+tan²α
=cosα(sinα/cosα)/sinα+tan²α
=1+tan²α
=1+sin²α/cos²α
=1+1/80
=81/80