题目

求值sin25π/6+cos25π/3+tan(-25π/4)+sin(-7π/3)×cos(-13π/6)-sin(-5π/6)×cos(-5π/3)

提问时间：2020-12-16

答案

sin25π/6+cos25π/3+tan(-25π/4)+sin(-7π/3)×cos(-13π/6)-sin(-5π/6)×cos(-5π/3)
=sin(4π+π/6)+cos(8π+π/3)+tan(-25π/4+6π)+sin(-7π/3+2π)×cos(-13π/6+2π)-sin(π-π/6)×cos(-5π/3+2π)
=sinπ/6+cosπ/3+tan(-π/4)+sin(-π/3)×cos(-π/6)-sin(π/6)×cos(π/3)
=sinπ/6+cosπ/3-tanπ/4-sinπ/3×cosπ/6-sin(π/6)×cos(π/3)
=1/2+1/2-1-√3/2×√3/2-1/2×1/2
=-3/4-1/4
=-1