Question

How do you work these out?
sec u- 1 / 1-cos u = sec u

sec x-cos x= sin x tan x

1/sin x - 1/csc x= csc x - sin x

Answer 1

remember that sec u = 1/cos u
and that csc u = 1/sin u
then for example

(1/cos u - 1) = 1
------------- -------
(1 - cos u) cos u

multiply both sides by cos u

(1 - cos u) = cos u
----------- -------
(1 - cos u) cos u

or

1 = 1 sure enough

for the second one, write sec as 1/cos and write tan as sin / cos
then multiply both sides by cos
and remember that sin^2 + cos^2 = 1

for the third one write csc is 1/sin