(C) We know that $\cos 2x = 1 - 2\sin^2 x$. Substituting this into the integral:$\int {\frac{{\cos 2x + 2{{\sin }^2}x}}{{{{\cos }^2}x}}dx} = \int {\fr

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(C) We know that $\cos 2x = 1 - 2\sin^2 x$. Substituting this into the integral:$\int {\frac{{\cos 2x + 2{{\sin }^2}x}}{{{{\cos }^2}x}}dx} = \int {\frac{{(1 - 2{{\sin }^2}x) + 2{{\sin }^2}x}}{{{{\cos }^2}x}}dx}$$= \int {\frac{1}{{{{\cos }^2}x}}dx}$$= \int {{{\sec }^2}x\,dx}$$= \tan x + c$