Question

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

Answer 1

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

Answer 2

cos(α-5π)= -cosα；tan(2π-α)= -tanα；cos(3π/2 +α)=sinα；
原式= -cosα*（ -tanα）/sinα+tan²α =1+tan²α =1/cos²α =1/（1-sin²α）=81/80