【1】化简:sin(a-5π)/cos(3π-a)×cos(π/2-a)/sin(a-3π)×cos(8π-a)/sin

4个回答

  • (1)=sin(a-π)/cos(π-a)*sin(a)/sin(a-π)*cos(a)/sin(-a)

    =sin(a)/cos(a)*sin(a)/[-sin(a)]*cos(a)/[-sin(a)]

    =1

    (2) f(x)=sin(nπ-x)cos(nx+x)/cos[(n+1)π-x]×tan(x-nπ)cot(nπ/2+x)

    当n为偶数时:f(x)=sin(-x)cos(x)/cos(π-x)*tan(x)*cot(x)

    =sinx

    当n为奇数时:f(s)=sin(π-x)cos(π+x)/cos(x)*tan(x)*cot(π/2+x)

    =sin(x)[-cos(x)]/cos(x)*tan(x)*[-tan(x)]

    =sin(x)[tan(x)]^2

    所以f(7/6π)=-1/2(n为偶数)

    =(-1/2)*(1/3)

    =-1/6