How do you simplify (sina+tana)/(1+cosa)?

1 Answer
Oct 11, 2016

(sin(a)+tan(a))/(1+cos(a))=tan(a)

Explanation:

(sin(a)+tan(a))/(1+cos(a)) = ((sin(a)+tan(a))(1-cos(a)))/((1+cos(a))(1-cos(a)))

=(tan(a)-sin(a)cos(a))/(1-cos^2(a))

=(tan(a)-sin(a)cos(a))/sin^2(a)

=(cot(a)(tan(a)-sin(a)cos(a)))/(cot(a)sin^2(a))

=(1-cos^2(a))/(cos(a)sin(a))

=sin^2(a)/(cos(a)sin(a))

=sin(a)/cos(a)

=tan(a)