$\cfrac{{\cos 2x + 2{{\sin }^2}x}}{{{{\cos }^2}x}}$
$\cfrac{{\cos 2x + 2{{\sin }^2}x}}{{{{\cos }^2}x}}$
Official Solution
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NCERT & Exemplar
: Let $I = \int {\cfrac{{\cos 2x + 2{{\sin }^2}x}}{{{{\cos }^2}x}}dx}$
$= \int {\cfrac{{\left( {{{\cos }^2}x + {{\sin }^2}x} \right) + 2{{\sin }^2}x}}{{{{\cos }^2}x}}} dx$
$= \int {\cfrac{{{{\cos }^2}x + {{\sin }^2}x}}{{{{\cos }^2}x}}} dx = \int {\cfrac{1}{{{{\cos }^2}x}}dx = \int {{{\sec }^2}xdx} } = \tan x + C$
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