Find the integral of \frac{cos^2⁡x-sin^2⁡x}{7 cos^2⁡x sin^2⁡x}.

Category: QuestionsFind the integral of \frac{cos^2⁡x-sin^2⁡x}{7 cos^2⁡x sin^2⁡x}.
Editor">Editor Staff asked 11 months ago

Find the integral of \frac{cos^2⁡x-sin^2⁡x}{7 cos^2⁡x sin^2⁡x}.
 
(a) –\frac{1}{7} (cot⁡x-tan⁡x)+C
 
(b) –\frac{1}{7} (cot⁡x-2 tan⁡x)+C
 
(c) –\frac{1}{7} (cot⁡x+tan⁡x)+C
 
(d) –\frac{1}{7} (2 cot⁡x+3 tan⁡x)+C
 
The question was posed to me during an interview.
 
I’m obligated to ask this question of Methods of Integration-2 topic in portion Integrals of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
Interview Questions and Answers, Database Interview Questions and Answers for Freshers and Experience

1 Answers
Editor">Editor Staff answered 11 months ago

Right choice is (c) –\frac{1}{7} (cot⁡x+tan⁡x)+C
 
Explanation: To find: \int \frac{cos^2⁡x-sin^2⁡x}{7 \,cos^2⁡x \,sin^2⁡x} dx
 
\int \frac{cos^2⁡x-sin^2⁡x}{7 \,cos^2⁡x \,sin^2⁡x} dx=\frac{1}{7} \int \frac{1}{sin^2⁡x}-\frac{1}{cos^2⁡x} dx
 
=\frac{1}{7} \int cosec^2 x-sec^2⁡x dx
 
=\frac{1}{7} (-cot⁡x-tan⁡x)+C
 
=-\frac{1}{7} (cot⁡x+tan⁡x)+C.