need cal 2 help before test please hurry?

Question

prove sech^2 x + tanh^2x =1 i know that sech = 1/cosh and i know what cosh and tanh equals with the e thing but how can you get them to cancel each other out?

Answer 1

Use the fact that cosh^2 x - sinh^2 x = 1. Divide by cosh^2 x and you will have your answer.

Answer 2

sech^2 x + tanh^2x =1

1/coshx+sinhx/coshx
=(1+sinhx )/coshx
=(1+(e^x-e^-x)/2)/( e^x+e^-x)/2)
=(2+e^x-e^-x)/(e^x+e^-x)