Write each expression in terms of sines andor cosines and th

Write each expression in terms of sines and/or cosines and then simplify.

(cos(x)tan(x)+1)(sin(x)1) =

(sec(x)1)(sec(x)+1) =

(1+cos(x))(1cot(x)sin(x)) =

Solution

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

2) (sec(x)1)(sec(x)+1) = (1 - cos(x))(cos(x)+1)

3) (1+cos(x))(1cot(x)sin(x)) = (1+cos(x))(1cos(x)sin(x)/sin(x)) = (1+cos(x))(1cos(x))