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

∫(1 cos x)/1+cos xdx =∫2sin^2 x/2/2 cos^2 x/2dx =∫ tan^2 x/2dx [∵ 1 cos x =2 sin^2 x/2 and 1+cos x=2 cos^2 x/2] =∫ ( sec^2 x/2 1 )dx [∴ tan^2 θ =sec^2 ...

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

Byju's Answer

Standard XII

Physics

Antiderivative

Find the inte...

Question

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

Open in App

Solution

$\int \frac{(1 - c o s x)}{1 + c o s x} d x = \int \frac{2 s i n^{2} \frac{x}{2}}{2 c o s^{2} \frac{x}{2}} d x = \int t a n^{2} \frac{x}{2} d x [∵ 1 - c o s x = 2 s i n^{2} \frac{x}{2} a n d 1 + c o s x = 2 c o s^{2} \frac{x}{2}] = \int (s e c^{2} \frac{x}{2} - 1) d x [∴ t a n^{2} θ = s e c^{2} θ - 1] = \int s e c^{2} \frac{x}{2} d x - \int 1 d x = \frac{t a n \frac{x}{2}}{\frac{1}{2}} - x + C (∴ \int s e c^{2} a s d x = \frac{t a n a x}{a}) = 2 t a n \frac{x}{2} - x + C$

Suggest Corrections

Similar questions

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

Q. Find the integrals of the functions

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

Q. Find the integrals of the functions

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

Q. Find the integrals of the function :

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

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

Join BYJU'S Learning Program

Find the integrals of the functions. ∫(1−cosx)1+cosxdx.

∫(1−cosx)1+cosxdx=∫2sin2x22cos2x2dx=∫tan2x2dx[∵1−cosx=2sin2x2 and 1+cosx=2cos2x2]=∫(sec2x2−1)dx [∴tan2θ=sec2θ−1]=∫sec2x2dx−∫1dx=tanx212−x+C(∴∫sec2asdx=tanaxa)=2tanx2−x+C

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