Integrals — Class 12 Maths Solution

ncert exercise SA NCERT,ex.7.2,Q.39,Page 305
Question

$\int {\cfrac{{dx}}{{{{\sin }^2}x{{\cos }^2}x}}}$equals

  • (a) $\tan x + \cot x + C$
  • (b) $\tan x - \cot x + C$
  • (c) $\tan x\cot x + C$
  • (d) $\tan x - \cot 2x + C$
Step-by-step Solution

Option b is correct

Let $I = \int {\cfrac{{dx}}{{{{\sin }^2}x{{\cos }^2}x}}} = \int {\cfrac{{{{\sin }^2}x + {{\cos }^2}x}}{{{{\sin }^2}x{{\cos }^2}x}}} dx$

$= \int {\left( {{{\sec }^2}x + \cos e{c^2}x} \right)} dx = \tan x - \cot x + C$

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NCERT & Exemplar solution for CBSE Class 12 Mathematics, Integrals. Curated by Sachin Sharma. Free for all students.