sina=asinb ,tana=btanb 得 1 /sinb=a/sina----(1),1/tanb=b/tana----(2)
(1)²-(2)²得：a²/sin²a-b²/tan²a=1 /sin²b-1/tan²b
=1 /sin²b-cos²b/sin²b=(1-cos²b)/sin²b=1
∴a²/sin²a-b²/tan²a=1
a²/sin²a-b²cos²a/sin²a=1
a²-b²cos²a=sin²a=1-cos²a
(b²-1)cos²a=a²-1
cos²a=(a²-1)/(b²-1)
cosa=正负√|(a²-1)/(b²-1)|