Question

若tan(7π+α)=α,求sin(α+3π)+cos(π-α)/sin(-α)-cos(π+α)的值

Answer 1

tan(7π+α)=α,

tanα=α,

sin(α+3π)+cos(π-α)/sin(-α)-cos(π+α)

=(-sinα-cosα)/(-sinα+cosα),(分子分母同除以cosα)

=(-tanα-1)/(-tanα+1)

=(-α-1)/(-α+1)

=(α+1)/(α-1)