Integrate the function \frac{\cos \left ( x+a \right )}{\sin \left ( x+b \right )} W.r.t.x.

 

 

 

 
 
 
 
 

Answers (1)

I= \int \frac{\cos \left ( x+a \right )}{\sin \left ( x+b \right )}\, dx\; \; = \int \frac{\cos \left \{ \left ( x+b \right )+\left ( a-b \right ) \right \}}{\sin \left ( x+b \right )}\: dx
   I= \int \left ( \frac{\cos \left ( x+b \right )\cos \left ( a-b \right )-\sin \left ( x+b \right )\sin \left ( a-b \right )}{\sin \left ( x+b \right )} \right )\, dx
   \Rightarrow \int \left ( \frac{\cos \left ( x+b \right )\cos \left ( a-b \right )}{\sin \left ( x+b \right )}-\frac{\sin \left ( x+b \right )\sin \left ( a-b \right )}{\sin \left ( x+b \right )} \right )\, dx
\Rightarrow \int\left \{ \cos \left ( a-b \right ) \cot \left ( x+b \right )-\sin \left ( a-b \right )\right \}\, dx
\Rightarrow \cos \left ( a-b \right )\log \left | \sin \left ( x+b \right ) \right |-x\: \sin \left ( a-b \right )+c

Preparation Products

Knockout NEET May 2021 (One Month)

An exhaustive E-learning program for the complete preparation of NEET..

₹ 14000/- ₹ 6999/-
Buy Now
Foundation 2021 Class 10th Maths

Master Maths with "Foundation course for class 10th" -AI Enabled Personalized Coaching -200+ Video lectures -Chapter-wise tests.

₹ 350/- ₹ 112/-
Buy Now
Foundation 2021 Class 9th Maths

Master Maths with "Foundation course for class 9th" -AI Enabled Personalized Coaching -200+ Video lectures -Chapter-wise tests.

₹ 350/- ₹ 112/-
Buy Now
Knockout JEE Main April 2021 (One Month)

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 14000/- ₹ 6999/-
Buy Now
Knockout NEET May 2021

An exhaustive E-learning program for the complete preparation of NEET..

₹ 22999/- ₹ 14999/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions