Question

证明：(1+sina+cosa)/(1-sina+cosa)=cosa/(1-sina)

Answer 1

证明

(1+sina+cosa)/(1-sina+cosa)

=[2cos²(a/2)+2sin(a/2)cos(a/2)]/[2cos²(a/2)-2sin(a/2)cos(a/2)]

分子分母同除以 2cos(a/2)

=[cos(a/2)+sin(a/2)]/[cos(a/2)-sin(a/2)]

分子分母同乘以cos(a/2)-sin(a/2)

=[cos²(a/2)-sin²(a/2)]/[cos(a/2)-sin(a/2)]²

=cosa/(1-sina)

得证.