Question

已知tana=2,求sin(pai-a)cos(2pai-a)sin(-a+3/2pai)/tan(-a-pai)sin(-pai-a)的值

Answer 1

sin(pai-a)cos(2pai-a)sin(-a+3/2pai)/tan(-a-pai)sin(-pai-a)
=sinacosa(-cosa)/(-tana*sina)
=(cosa)^2/tana
=1/[tana(1+(tana)^2)]
=1/(2*5)=1/10

Answer 2

原式=-sinacosacosa/(-tanasina)
=cos^2a/2
=cos^2a/2-1/2+1/2
=1/2cos2a+1/2
=1/2(1-tan^2a)/(1+tan^2a)+1/2
=1/2*(-3)/5+1/2
=1/5

Answer 3

sin(π-a)cos(2π-a)sin(-a+3π/2)/tan(-a-π)sin(-π-a)
=sina*cosa*(-cosa)/[-tana*sina]
=(cosa)^2/tana=(cosa)^2/2
而(sina)^2+(cosa)^2=1=5(cosa)^2
则(cosa)^2=1/5
所以上式=1/10

Answer 4

tana=2
sin(π-a)cos(2π-a)sin(-a+3/2π) / {tan(-a-π) sin(-π-a) }
= sina cosa (-cosa) / {(-tana)sina}
= cos^2a / tana
= {1/(1+tan^2a)}/ tana
= 1/{ (1+tan^2a) tana}
= 1/{(1+2^2)*2}
= 1/10