tan [arccos(x) ] / [1 - sin(x) ]
1) First work the numerator, which is the confussing part
x = cos(y) => arccos(x) = y
tan [arccos(x) ] = tan (y) = sin (y) / cos (y)
using the fundamental identity
[cos(y)] ^2 + [sin(y)}^2 = 1 => sin (y) = √(1 - [cos(y)]^2 ) = √(1 - x^2)
=> tan (y) = sin(y) / cos(y) = √(1-x^2) / x ... this is the numerator
2) write the complete fraction using the numerator just found
[√(1 - x^2) / x] / (1 - sin(x) ) = √(1 - x^2) / [x (1 - sin(x) ]
Answer: √(1 - x^2) / [x (1 - sin(x) ]
