Find the integrals of the functions-cos x-1-cos x d x

∫cos x/1+cos xdx = ∫1 1+cos x/1+cos xdx [add and subtract 1 in numerator] =∫1+cos x/1+cos xdx ∫1/1+cos xdx =∫ 1 dx ∫1/2 cos^2 x/2dx =∫ 1dx 1/2∫ sec^2 x/2dx ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Trigonometric Ratios of Compound Angles

Find the inte...

Question

Find the integrals of the functions.
$\int \frac{c o s x}{1 + c o s x} d x .$

Open in App

Solution

$\int \frac{c o s x}{1 + c o s x} d x = \int \frac{1 - 1 + c o s x}{1 + c o s x} d x$
[add and subtract 1 in numerator]
$= \int \frac{1 + c o s x}{1 + c o s x} d x - \int \frac{1}{1 + c o s x} d x = \int 1 d x - \int \frac{1}{2 c o s^{2} \frac{x}{2}} d x = \int 1 d x - \frac{1}{2} \int s e c^{2} \frac{x}{2} d x = x - \frac{1}{2} .2 t a n \frac{x}{2} + C = x - t a n \frac{x}{2} + C (∴ \int s e c^{2} a x d x = \frac{t a n a x}{a})$

Suggest Corrections

Similar questions

Find the integrals of the functions.
$\int \frac{(1 - c o s x)}{1 + c o s x} d x .$

Find the integrals of the functions.
$\int \frac{1}{c o s (x - a) c o s (x - b)} d x .$

Q. Find the integrals of the function :

\frac{1 - cos x}{1 + cos x}

Q. Integrate:

\int \frac{cos x}{1 + cos x} d x

Q. Integrate

\int \frac{1 - cos x}{1 + cos x} d x

Join BYJU'S Learning Program

Find the integrals of the functions. ∫cosx1+cosxdx.

∫cosx1+cosxdx=∫1−1+cosx1+cosxdx [add and subtract 1 in numerator] =∫1+cosx1+cosxdx−∫11+cosxdx=∫1dx−∫12cos2x2dx=∫1dx−12∫sec2x2dx=x−12.2tanx2+C=x−tanx2+C(∴∫sec2axdx=tanaxa)

Find the integrals of the functions.
$\int \frac{c o s x}{1 + c o s x} d x .$