Statement -1: If `xltsqrt(e )`then
`cot^(-1){log(e//x^(2))/log(ex^(2))}+cot^(-1){log(ex^(4))/log(e^(2)//x^(2)))}=pi-tan^(-1)3`
statement 2:`tan^(-1)(x+y)/(1-xy)=tan^(-1)x+tan^(-1)y if xylt1`

Options

A. Statement-1 is is True, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True.

Explanation

statement 2 is true (see history )
Now
`cot^(-1){log(e//x^(1))/log(ex^(2))}+cot^(-1){logex^(4))/log(e^(2)//x^(2)))}`
`=cot^(-1){(1-2logx)/(1+2 logx)}+cot^(-1){(1+4logx)/(2-2logx)}`
`=tan^(-1)(1+2 logx)/(1-23logx)+(pi)/(2)tan^(-1)((1/2+2logx)/(1-1/2xx2logx)`
`=tan^(-1)(1+2logx)/(1-2logx)+(pi)/(2)-tan^(-1)((1/2+2logx)/(1-1/2xx2logx))`
`=tan^(-1)(1)+tan^(-1)(2 logx)+(pi)/(2)-tan^(-1)1/2-tan^(-1)(2 logx)`
if `2 log x l 1 and log x lt 1`
`=(3pi)/(4) -tan^(-1)1/2 if x lt sqrt(e )`
`=pi -(tan^(-1)1+tan^(-1)1/2)=pi tan^(-1)3`
So statement 1 is alos true also statement -2 is a correct explanation fro statement-1