Simplify \[\large \frac{\tan \beta}{\sec \beta +1} - \frac{\sec \beta -1}{\tan \beta}\]
+130081 I always find it easiest to convert things to sine and cosine....so....
sin / cos sin /cos sin
_______ = _____________ = ________
1/cos + 1 (1 + cos) /cos 1 + cos
sec - 1 1/cos -1 (1 -cos) /cos 1 -cos
_______ = ________ = __________ = _____
tan sin /cos sin /cos sin
So we have
sin 1 -cos
_________ - _________ =
1 + cos sin
sin^2 - ( 1 -cos) (1 + cos)
_______________________ =
sin (1 + cos)
sin^2 - ( 1 -cos^2)
________________ =
sin (1 + cos)
sin^2 + cos^2 - 1
__________________ =
sin (1 + cos)
1 - 1
___________ = 0
sin ( 1 + cos)
