Question

若sinacosa<0,sinatana<o,化简(√1-sina/2)/(1+sina/2)+√(1+sina/2)/(1-sina/2)

Answer 1

解：∵sinacosa<0
∴sin2a<0
∴π<2a<2π
∴π/2<a<π;
又∵sinatana<0
即(sina)^2/cosa<0
∴cosa<0
∴π/2<a<3π/2
∴π/2<a<π
∴π/4<a/2<π/2
∴cosa/2>0,1+sina/2>0,1-sina/2>0
√[1sin(a/2)]/(1+sin(a/2)]+√[1+sin(a/2)]/[1-sin(a/2)]=√[cos(a/2)]^2/[1+sin(a/2)]^2+√[cos(a/2)]^2/[1-sin(a/2)]^2

={cos(a/2)/[1+sin(a/2)]}+cos(a/2)/[1-sin(a/2)]
=2/cos(a/2)
=2sec(a/2)