Question

How do you prove `sin(t)/cos(t) + cos(t)/sin(t)= 1/(sin(t)cos(t))`?

Answer 1

Take the LCM

`(sin^2(t) + cos^2(t))/(cos(t)sin(t)) = 1/(sin(t)cos(t)`

Use the pythagorean identity

`sin^2(t) + cos^2(t) = 1`

`1/(cos(t)sin(t)) = 1/(sin(t)cos(t))`