starting with cos^2(x)+sin^2(x)=1 and using your knownledge of the quotient and reciprocal identities. derive an equivlaent identity in terms of tan(x) and sec(x)
cos^2(x)+sin^2(x)=1 divide everything by cos^2x
1 + sin^x /cos^x = 1/cos^2x
1 + tan'2x = sec^2x
So
sec^2x - tan'2x = 1 = sin^2x + cos^2x
And these identites are equivalent..... {I assume that's what you wanted }