Question #359ad

1 Answer
Dec 6, 2017

arctan(cosx/(1-sinx))=pi/4+x/2

Explanation:

cosx/(1-sinx)

=[(cos(x/2))^2-(sin(x/2))^2]/(cos(x/2)-sin(x/2))^2

=[(cos(x/2)-sin(x/2))*(cos(x/2)+sin(x/2))]/(cos(x/2)-sin(x/2))^2

=(cos(x/2)+sin(x/2))/(cos(x/2)-sin(x/2))

=(1+tan(x/2))/(1-tan(x/2))

=tan(pi/4+x/2)

Thus,

arctan(cosx/(1-sinx))=pi/4+x/2