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I'm working on this problem:

y = sin^2(x) / cos^2 (x)

what is dy/dx?

In the solutions it says to convert (sin(x)/cos(x))^2=tan^2(x)

And the answer is dy/dx = 2sec^2(x)tanx

However, using the quotient rule, I got this answer:

dy/dx =[ (2sin(x)cos(x))cos^2(x) - (sin^2x)2(cos(x))(-sin(x))] / cos^2(x)

=[2sin(x)cos^2(x)+2sin^3(x)]/cos^2 (x)

Does this mean

[2sin(x)cos^2(x)+2sin^3(x)]/cos^2 (x) = 2sec^2(x)tanx ?