Question

Let `f(x)=2 tan^(-1)((1-x)/(1+x))`
A. Statement-1 True statement -1 is True,Statement -2 is True statement -2 is a correct explanation for Statement-5
B. Statement-1 True statement -1 is True,Statement -2 is True statement -2 is not a correct explanation for Statement-5
C. Statement-1 True statement -1 is True,Statement -2 is False
D. Statement-1 is False ,Statement -2 is True

Answer 1

Correct Answer - A
`f(x)=2tan^(-1)""(1-x)/(1+x)(tan^(-1)-tan^(-1)x)"-="pi/2-2tan^(-1)""x`
`rArr f(x)=-(2)/(1+x^2)lt0 for all x in [0,1]`
`rArr f(x)` decreases on [0,1]
`rArr ` Range of `f=[f(1),f(0)]=[0,pi//2]`
Hence both the statements are ture and statement are ture and statement -2 is a correct explanation of statement - 1