Home
Class 12
MATHS
int0^a log (cota+ tanx)dx where a in (0,...

`int_0^a log (cota+ tanx)dx` where `a in (0,pi/2)` is (A) `alnsina` (B) `-alnsina` (C) `-alncosa` (D) none of these

A

`a ln (sina)`

B

`-a ln (sina)`

C

`-a ln (cos a)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`I=int_(0)^(a)ln(cot a +tanx)dx`
`=int_(0)^(a)ln((cos(a0x))/(sina cosx))dx" (1)"`
`therefore" "I=int_(0)^(a)ln((cosx)/(sina cos(a-x)))dx" (2)"` Adding (1) and (2) we get `2I=int_(0)^(a)ln((1)/(sin^(2)a))dx`
`=-2int_(1)^(a)ln(sina)dx`
`=-2aln(sina)`
Promotional Banner

Similar Questions

Explore conceptually related problems

int_(0)^((pi)/(2)) log (cotx)dx is :

Solve tanx >cotx , where x in [0,2pi]dot

int_0^oo(x dx)/((1+x)(1+x^2)) is equal to (A) pi/4 (B) pi/2 (C) pi (D) none of these"

Prove that int_(0)^((pi)/(2)) log ( tan x ) dx = 0

Prove that int_(0)^((pi)/(2)) sin 2x log ( tan x ) dx = 0

If y=(log)_(sinx)(tanx),t h e n(((dy)/(dx)))_(pi/4)"is equal to" (a) 4/(log2) (b) -4log2 (c) (-4)/(log2) (d) none of these

The value of int_0^(pi/2) sin|2x-alpha|dx, where alpha in [0,pi], is (a) 1-cos alpha (b) 1+cos alpha (c) 1 (d) cos alpha

The value of int_(1/e)^(tanx)(tdt)/(1+t^2)+int_(1/e)^(cotx)(dt)/(t(1+t^2)), where x in (pi/6,pi/3) , is equal to: (a)0 (b) 2 (c) 1 (d) none of these

The value of 3^((log)_4 5)-5^((log)_4 3) is 0 (b) 1 (c) 2 (d) none of these