2 x - 2 x si n 2 x 2 x dx is equals to

Option a is correct Let I = 2 x - 2 x si n 2 x 2 x dx = 2 x - e c 2 x )dx = x + x + C

Integrals — Class 12 Maths Solution

ncert exercise SA NCERT,ex.7.3,Q.23,Page 307

Question

$\int {\cfrac{{{{\sin }^2}x - {{\cos }^2}x}}{{si{n^2}x{{\cos }^2}x}}dx}$ is equals to

(a) $\tan x + \cot x + C$
(b) $\tan x + {\mathop{\rm cosec}\nolimits} x + C$
(c) $- \tan x + \cot x + C$
(d) $\tan x + \sec x + C$

Step-by-step Solution

Option a is correct

Let $I = \int {\cfrac{{{{\sin }^2}x - {{\cos }^2}x}}{{si{n^2}x{{\cos }^2}x}}dx}$
$= \int {\left( {{{\sec }^2}x - \cos e{c^2}x} \right)dx} = \tan x + \cot x + C$

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