Question

1.若sin2x=4/5,则tanx^2+cot^2=

Answer 1

(tanx)^2+(cotx)^2=(sinx/cosx)^2+(cosx/sinx)^2=[(sinx)^4+(cosx)^4]/(sinxcosx)^2={[(sinx)^2+(cosx)^2]^2-2(sinx)^2*(cosx)^2}/(sinxcosx)^2(sinx)^2+(cosx)^2=1,sin2x=2sinxcosx=4/5,sinxcosx=2/5代入上式得17/4...