1800-150-456-789
FlagBACK
Flag Integral Calculus> integral Of cos x / (1+cosx+sinx) dx [lim...
question mark

integral Of cos x / (1+cosx+sinx) dx [lim- 0 to pie ]

Suriya S , 7 Years ago
Grade 12
anser 1 Answers
Arun

Last Activity: 7 Years ago

 
convert x into half angle- like (x/2)
put cos x=cos2x/2-sin2x/2 [because cos2x= cos2x- sin2x]
write (1+cosx) as 2cos2x/2 [ cos 2x+1= 2 cos2 x/2]
and sinx as( 2 sin x/2 cos x/2) [because sin 2x= 2sinx cosx]
then solve it
I =∫(cos2x/2- sin2x/2) /2 cos2x/2 +2 sin x/2 cosx/2 [ limit o to pi/2]
I= 1/2∫(cos x/2+sin x/2) ( cosx/2- sin x/2) / cos x/2( cosx/2 +sin x/2) [limit from 0 tp pi/2]
{ take 1/2 cosx x/2 common from denominator}
I =1/2∫ (cos x/2 -sin x/2) /cos x/2 [limit from 0 to pi/2]
I = 1/2∫ (1- tan x/2)dx [limit from 0 to pi/2]
I =1/2 [x- 2 Log sec x/2] [ limit from 0 to pi/2]
I = 1/2 [pi/2 - log 2]
hope ,this is only the ans !!

Provide a better Answer & Earn Cool Goodies

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free

Other Related Questions on integral calculus

question mark
The area of a square field is 640000cm2.what is its area in hectares
integral calculus
1 Answer Available

Last Activity: 2 Years ago

question mark
Please solve this integration. I am facing difficulty in it
 How to solve this. Please solve anyone. Humble request
integral calculus
0 Answer Available

Last Activity: 2 Years ago

question mark
Using laplace transform, solve d2y/dt2 + dy/dt = t2 +2t given that y=4 and y’=-2 and t=0
integral calculus
0 Answer Available

Last Activity: 3 Years ago

question mark
how to solve this?
this is interger type question .
integral calculus
0 Answer Available

Last Activity: 3 Years ago