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Question

The derivative of f(x) defined by f(x)=tan1(1cos x1+cos x), π<x<π
is 


Your Answer
A
1, if 0<x<π
Your Answer
B
1, if π<x<0
Correct Answer
C
12, if 0<x<π
Correct Answer
D
12, if π<x<0

Solution

The correct options are
C 12, if 0<x<π
D 12, if π<x<0
Given that,
Let y=tan1(1cos x1+cos x), π<x<πThen, y=tan1 2 sin2 x/22 cos2 x/2=tan1(tan x2y=tan1(tan x2) ,    if tan x20tan1(tan x2) ,    if tan x2<0y=(x2 ,      if 0x<πx2 ,      if π<x<0dydx=12 ,      if 0x<π12 ,      if π<x<0

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