tanα=2,求sin(π-α)cos(2π-α)sin(-α+ 3π/2)/tan(-α-π)si

tanα=2,求sin(π-α)cos(2π-α)sin(-α+ 3π/2)/tan(-α-π)si

sin(π-α)cos(2π-α)sin(-α+ 3π/2)/tan(-α-π)sin(-π-α)=sinαcosα(-cosα) / (-tanα)sinα=(cosα)^2 / tanα=(cosα)^2 / 2=[(1/2)(1+cos2α)] / 2=(1/4)(1+cos2α)=(1/4) + (1/4)×[1-(tanα)^2 / 1+(tanα)^2]=(1/4) + (1/4)×(-3/5)=1/10======以下答案可供参考======供参考答案1:sin（π-α）= sinα cos（2π-α）= cosα sin（-α+3π/2）= -cosαtan（-α-π）= -tan（α+π）= -tanα = -2sin(-π-α)= -sin(π+α) = sinα 所以，原题=sinα* cosα *（ -cosα）/ - 2 sinα= 1/2（cosα）^2 = 1/4(cos2α+1)cos2α=[1-tan(α)^2]/{1+[tan(α)]^2}=[1-4]/{1+4}=-3/5原式=1/4(-3/5+1)=1/10供参考答案2:原式=sinacosa(-cosa)/(-tanasina)=cosacosa/tana=1/secasecatana=1/(1+tanatana)tana=1/(1+4)2=1/10供参考答案3:sin(π-α)cos(2π-α)sin(-α+ 3π/2)/tan(-α-π)sin(-π-α)=sinαcosαsin(-α)/tan(-α)sinα=(cosα)^2=1/2(cos2α+1)因为cos2α=[1-tan(α)^2]/{1+[tan(α)]^2}=[1-2^2]/{1+2^2}=-3/5所以，原式=1/2(-3/5+1)=1/5供参考答案4:所以sinα=-2√2/3 由诱导公式 cot(-α-π)=-cotα sin(2π α)=sinα cos(-α)=cosα 所以原式=-cotαsinα/cosαtanα =-cotα*(sin