Question 173675
You need to use the following identity twice: 

sin^2(s) + cos^2(s) = 1
OR sin^2(s) = 1 - cos^2(s)
OR cos^2(s) = 1 - sin^2(s)

Start by replacing sin^2(s) with 1 - cos^2(s) on the left hand side of the equation:

tan^2(s)*(1-cos^2(s)) = tan^2(s) + cos^2(s) - 1

Then, distribute:

tan^2(s) - tan^2(s)*cos^2(s) = tan^2(s) + cos^2(s) - 1

Since tan^2(s) = {{{sin^2(s)/cos^2(s)}}}, simplify the left hand side to:

tan^2(s) - sin^2(s) = tan^2(s) + cos^2(s) - 1

Then, replace cos^2(s) with 1 - sin^2(s) on the right hand side:

tan^2(s) - sin^2(s) = tan^2(s) + 1 - sin^2(s) - 1

tan^2(s) - sin^2(s) = tan^2(s) - sin^2(s)

So they are equal!