Advertisements
Advertisements
Question
Find the integrals of the function:
`(1-cosx)/(1 + cos x)`
Advertisements
Solution
Let `I = int (1 - cos x)/(1 + cos x) dx`
`= int (2 sin^2 x/2)/(2 cos^2 x/2) dx`
`= int tan^2 x/2 dx`
`= int (sec^2 x/2 - 1) dx`
`= [(tan x/2)/(1/2) - x + C]`
`= 2 tan x/2 - x + C`
APPEARS IN
RELATED QUESTIONS
Evaluate :`int_(pi/6)^(pi/3) dx/(1+sqrtcotx)`
Find the integrals of the function:
`cos x/(1 + cos x)`
Find the integrals of the function:
sin4 x
Find the integrals of the function:
`(cos 2x - cos 2 alpha)/(cos x - cos alpha)`
Find the integrals of the function:
`(cos x - sinx)/(1+sin 2x)`
Find the integrals of the function:
`1/(sin xcos^3 x)`
Find the integrals of the function:
`(cos 2x)/(cos x + sin x)^2`
Find the integrals of the function:
sin−1 (cos x)
`int (sin^2x - cos^2 x)/(sin^2 x cos^2 x) dx` is equal to ______.
Find `int (sin^2 x - cos^2x)/(sin x cos x) dx`
Find `int((3 sin x - 2) cos x)/(13 - cos^2 x- 7 sin x) dx`
Evaluate : \[\int\limits_0^\pi \frac{x \tan x}{\sec x \cdot cosec x}dx\] .
Find `int_ (sin "x" - cos "x" )/sqrt(1 + sin 2"x") d"x", 0 < "x" < π / 2 `
Find `int_ (sin2"x")/((sin^2 "x"+1)(sin^2"x"+3))d"x"`
Find the area of the triangle whose vertices are (-1, 1), (0, 5) and (3, 2), using integration.
Find: `int_ (cos"x")/((1 + sin "x") (2+ sin"x")) "dx"`
Evaluate `int tan^8 x sec^4 x"d"x`
Find `int x^2tan^-1x"d"x`
`int (sin^6x)/(cos^8x) "d"x` = ______.
Evaluate the following:
`int ((1 + cosx))/(x + sinx) "d"x`
Evaluate the following:
`int ("d"x)/(1 + cos x)`
Evaluate the following:
`int "e"^(tan^-1x) ((1 + x + x^2)/(1 + x^2)) "d"x`
`int sinx/(3 + 4cos^2x) "d"x` = ______.
`int (cos^2x)/(sin x + cos x)^2 dx` is equal to
What does integration using trigonometric identities mean?
Which identity is used for the product of sine and cosine?
What is \(\int \cos^2 x\,dx\)?
Applying the product-to-sum identity to \(\sin 2x\cos 3x\) gives which expression?
What is \(\int \sin 2x\cos 3x\,dx\)?
Which procedure is recommended when an identity can simplify a complicated trigonometric expression?
After a trigonometric expression has been simplified, how should it be integrated?
