求证tana+1/tan(π/4+a/2)=1/cosa

2个回答

  • 左=sinA/cosA + cos(π/4+A/2) /sin(π/4+A/2)

    =sinA/cosA + [cosπ/4 cosA/2-sinπ/4 sinA/2]/[sinπ/4 cosA/2+sinA/2cosπ/4]

    =sinA/cosA + [cosA/2- sinA/2]/[ cosA/2+sinA/2]

    =sinA/cosA + [cosA/2- sinA/2][cosA/2- sinA/2]/[ cosA/2+sinA/2][cosA/2- sinA/2]

    =sinA/cosA + [cos^2 A/2- 2sinA/2cosA/2-+sin^2 A/2]/cos^2 A/2- sin^2 A/2]

    =sinA/cosA +(1-sinA)/cosA

    =1/cosA =右边