Question

Question #7bd62

Answer 1

#(tan^2x )(csc^2x -1) =(tan^2x)((1+cot^2x)-1) =tan^2xcot^2x=1#

Explanation:

The basic "Pythagoras" trig relationship is:
`sin^2x+cos^2x=1`, from which you get the other two by dividing both sides either by `sin^2x` or `cos^2x`:
`1+cot^2x=csc^2x` and `tan^2x+1=sec^2x`.

Remember that by definition `cotx=1/tanx`, `secx=1/cosx` and `csc x=1/sinx`.