Question

How do you prove `(sec(u) - tan(u))(csc(u)+1)=cot(u)`?

Answer 1

Left side terms in parentheses need to be multiplied as sec u csc u- csc u tan u +sec u -tan u and then write it in terms of sin and cos.

=`1/(sin u cos u) - 1/cos u + 1/cos u - sin u/ cos u`

=`(1 - sin^2 u)/(sin u cos u)`

=`cos^2 u/(sin u cos u)`

=`cos u/ sin u`

= cot u