高一数学三角函数化简:sin50du(1+genhao3tan10du)du是度数,genghao是根号,不好意思,弄错

3个回答

  • sin50°*(1+根号3×tan10°)

    =sin50°*(1+根号3*sin10°/cos10°)

    =sin50°/cos10°*(cos10°+根号3*sin10°)

    =2*sin50°/cos10°*(1/2*cos10°+根号 3/2*sin10°)

    =2*sin50°/cos10°*(sin30°*cos10°

    +cos30°*sin10°)

    =(2*sin50°/cos10°)* sin40°

    =(2*cos40°/cos10°)* sin40°

    =(2* sin40°cos40°)/ cos10°

    =sin80°/cos10°

    =cos10°/cos10°

    =1

    =sin50[1+(sin60/cos60)*(sin10/cos10)]

    =sin50[1+(sin60*sin10)/(cos60*cos10)]

    =sin50[(sin10*sin60+cos10*cos60)/(cos10*cos60)]

    =sin50[cos(60-10)/(cos10*cos60)]

    =sin50[cos50/(cos10*cos60)]

    =(sin50*cos50)/(cos10*cos60)

    =sin100/(2*cos10*cos60)

    =sin80/(2*cos10*cos60)

    =cos10/(2*cos10*cos60)

    =1/(2cos60)

    =1