Question

Write the following function in the simplest form:

`tan^(-1) (sqrt((1 - cos x)/(1 + cos x)))`, 0 < x < π

Answer 1

`tan^(-1) (sqrt((1 - cosx)/(1 + cosx)))`

= `tan^(-1) (sqrt((2sin^2  x/2)/(2cos^2  x/2)))` 

= `tan^(-1) ((sin  x/2)/(cos  x/2)) `

= `tan^(-1) (tan  x/2)`

= `x/2`