tan675°+cot765°-tan(-300°)-cot(-690°)=?

解tan675°+1/tan765°-sin(-5π/2)+1/cos(-23π/6)
=tan(720°-45°)+1/tan(720°+45°)+sin(5π/2)+1/cos(23π/6)
=tan(-45°)+1/tan(45°)+sin(2π+π/2)+1/cos(4π-π/6)
=-tan(45°)+1/1+sin(π/2)+1/cos(-π/6)
=-1+1+1+1/(cos(π/6))
=1+1/(√3/2)
=1+2√3/3

tan675°+cos765°-sin（-5π/2）+sec（-23π/6）
=tan（675°-720°）+cos（765°-720°）-sin（4π-5π/2）+sec（4π-23π/6）
=tan（-45°）+cos45°-sin（3π/2）+secπ/6
=-1+√2/2+1+2√3/3
=2√3/3+√2/2
cosα*secα＝1

sin120°=cos30°
cos750°=cos30°
sin(-690°)=sin30°
cos(-660°)=cos60°
tan675°=tan45°
cot765°=cot45°
tan1020°=-tan60°
cot(-1230°)=cot30°
sin120°+cos750°+sin(-690°)cos(-660°)+tan675°+cot765°-tan1020°+cot(-1230°)
=cos30°+cos30°+sin30°cos60°+tan45°+cot45°+tan60°+cot30°
=2cos30°+sin30°sin30°+2+2tan60°
=√3+1/4+2+2√3
=3√3+9/4

1) tan675°+tan765°+tan(-300°)+tan(-690°)+tan1080°
= tan(720-45) + tan(720+45) + tan(-300+360) + tan(-690+720) +tan (3*360)
= tan(-45) + tan45 + tan 60 + tan 30 = √3 + √3/3
(2)sin(π-a)cos(3π-a)tan(-a-π)tan(a-2π)/tan(4π-a)sin(5π+a)
= sina*(-cosa)(-tana)tana/ [(-tana)(-sina)]
= sina sina tana/ (tana sina) = sina

∵tan(x+k∏)=tanx
∴原式为 tan135°+ tan45°-tan30°+ tan30°=0

原式=tan(3*180+135)+cos(2*360+45)-tan(-2*180+60)+cos(-2*360+30)
=tan135+cos45-tan60+cos30
=-1+√2/2-√3+√3/2
=(-2+√2-√3)/2