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

Question

4161 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-09T16:23:04

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

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