Question

已知sinx=2√5/5,求tan(π+x)+sin(5π/2+x)/cos(5π/2-x)

Answer 1

解答:

∵ sinx=2√5/5,

∴ cos²x=1-sin²x=1-4/5=1/5

∴ cosx=±√5/5,

tan(π+x)+sin(5π/2+x)/cos(5π/2-x)

=tanx+ (cosx)/sinx

=sinx/cosx+cosx/sinx

=(sin²x+cos²x)/(sinxcosx)

=1/(sinxcosx)

=1/[(2√5/5)*(±√5/5)]

=±1/(2/5)

=±5/2