已知tan(π-α)=a的平方,|cos(π-α)|=-cosα,则1/cos(π+α)的值为

Question

已知tan(π-α)=a的平方,|cos(π-α)|=-cosα,则1/cos(π+α)的值为

Answer 1

∵|cos(π-α)|=-cosα
==>|cosα|=-cosα
∴cosα-tanα=a²
==>tanα=-a²
==>sinα/cosα=-a²
==>sinα=-a²cosα
∴(-a²cosα)²+cos²α=1
==>(1+a^4)cos²α=1
==>cosα=-1/√(1+a^4)
故1/cos(π+α)=1/(-cosα)
=1/(1/√(1+a^4))
=√(1+a^4)