integrate 1/1-tanx

CBSE, JEE, NEET, CUET

Question Bank, Mock Tests, Exam Papers

NCERT Solutions, Sample Papers, Notes, Videos

Install Now

integrate

1/1-tanx

Posted by Vishaal Velu 8 years, 3 months ago

CBSE > Class 12 > Mathematics

1 answers

Naveen Sharma 8 years, 3 months ago

Ans. $\int {1\over 1-tan x}dx$

$=> \int {1\over 1-{sinx\over cosx}}dx$

$=> \int {cos x\over cos x - sinx}dx$

Multiply and Divide By 2, We Get

$=> {1\over2}\int {2cos x\over cos x-sinx}dx$

$=> {1\over2}\int {2cos x+sin x - sin x \over cos x-sinx}dx$

$=> {1\over2}\int {(cos x+sin x)+(cos x - sin x )\over cos x-sinx}dx$

$=> {1\over2}\int {(cos x+sin x)\over cosx-sinx}dx+{1\over2}\int{ (cos x - sin x )\over cos x-sinx}dx$

$=> {1\over2}\int {(cos x+sin x)\over cosx-sinx}dx+{1\over2}\int dx$

Put (cos x - sin x) = t, then

(-sin x - cos x)dx = dt or -(cos x +sin x) dx = dt

$=> {1\over2}\int {-dt\over t }+{1\over2}\int dx$

$=> -{1\over 2} log t + {1\over 2} x + C$

$=> -{1\over 2} log (cos x-sin x) + {1\over 2} x + C$

1Thank You

ANSWER

Related Questions

function f is defined as f(x) = {2x+2, x<2; k, x=2; 3x, x>2} find the value of k for which the function f is continuous at x=2

Posted by Krishnanjali Nigam 11 months, 2 weeks ago

CBSE > Class 12 > Mathematics

2 answers

What is the maximum value of sinx + cos x

Posted by Xxxxxx Xx 10 months, 1 week ago

CBSE > Class 12 > Mathematics

3 answers

Find all vectors of magnitude 10√3 that are perpendicular to the plane of i+2j+k and -i+3j+4k

Posted by Sanjay Kumar 10 months, 4 weeks ago

CBSE > Class 12 > Mathematics

0 answers

Prove that tan–¹ (x+1) + tan–¹(x-1) = tan–¹ 8/31

Posted by Ananya Singh 11 months, 3 weeks ago

CBSE > Class 12 > Mathematics

0 answers

Find the second order derivatives of the functions x²+3x+2

Posted by Sanjna Gupta 10 months, 1 week ago

CBSE > Class 12 > Mathematics

4 answers

Y= 1/2 [tan¯¹(2x/1-x²) + 2tan¯¹(1/x)

Posted by Charu Baid 10 months, 2 weeks ago

CBSE > Class 12 > Mathematics

0 answers

Project on to minimise the cost of the food, meeting the dietary requirements of the staple food of the adolescent students of your school. Task to be done 1. Make a survey of atleast 100 people to find the staple food they consume on daily basis. 2. Select two food items constituting one cereal and one pulse. 3. Find from dietician minimum requirement of protein and carbohydrates for an andolescent and also find the content of protein and carbohydrates in 1 Kg of selected cereal and pulse from the market. 4. Find the minimum cost of the selected cereal and pulse from market. 5. formulate the corresponding linear programming problem. 6. solve the problem graphically. 7. Interpret the result.

Posted by Guruansh Singh Malra 5 months, 2 weeks ago

CBSE > Class 12 > Mathematics

0 answers

Y=sin√ax^2+√bx+√c

Posted by Karan Kumar Mohanta 10 months, 2 weeks ago

CBSE > Class 12 > Mathematics

0 answers

Three friends Ravi Raju

Posted by Sneha Pandey 11 months ago

CBSE > Class 12 > Mathematics

0 answers

What is the maximum value of the function sin x + cosx

Posted by Xxxxxx Xx 10 months, 1 week ago

CBSE > Class 12 > Mathematics

0 answers

myCBSEguide

CBSE, JEE, NEET, CUET

myCBSEguide

Test Generator

CUET Mock Tests

Download myCBSEguide App

All Courses

Other Websites

CBSE Courses

Resources

Corporate

NCERT Solutions

CBSE Sample Papers