Question

计算（1）sin420度*cos750度+sin（-330度）*cos（-660度） tan675度+tan765度-tan（-330度）+tan（-690度

（3）sin25TT/6+cos25TT/3+tan（-25TT/4）要过程

Answer 1

解(1)：原式=sin(360°+60°)×cos(2×360°+30°)-sin330°×cos660°
=sin60°×cos30°-sin(360°-30°)×cos(3×360°-60°)
=sin60°×cos30°-(-sin30°)×cos(-60°)
=sin60°×cos30°+sin30°×cos60°
=√3/2×√3/2+1/2×1/2
=3/4+1/4
=1

解(2)：原式=tan(2×360°-45°)+tan(2×360°+45°)+tan330°-tan690°
=-tan45°+tan45°+tan(360°-30°)-tan(2×360°-30°)
=-tan30°-(-tan30°)
=-tan30°+tan30°
=0

解3：原式=sin[4π+(π/6)]+cos[8π+(π/3)]+tan[-6π+(-π/4)]
=sin(π/6)+cos(π/3)+tan(-π/4)
=sin(π/6)+cos(π/3)-tan(π/4)
=1/2+1/2-1
=0