1+sina/cosa如何化简成cot(π/4-a/2)

1个回答

  • 1+sina/cosa=(sin²a/2+cos²a/2+2sina/2cosa/2)/(cos²a/2-sin²a/2)

    =(sina/2+cosa/2)²/[(cosa/2+sina/2)(cosa/2-sina/2)]

    =(sina/2+cosa/2)/(cosa/2-sina/2)

    =[√2(√2/2sina/2+√2/2cosa/2)]/[√2(√2/2cosa/2-√2/2sina/2)]

    =(sina/2cosπ/4+sinπ/4cosa/2)]/(cosπ/4cosa/2-sinπ/4sina/2)

    =sin(a/2+π/4)/cos(π/4+a/2)

    =tan(a/2+π/4)

    =cot[π/2-(a/2+π/4)]

    =cot(π/4-a/2)