Home
Class 12
MATHS
Statement -1: If xltsqrt(e )then cot^...

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`

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.

Text Solution

Verified by Experts

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
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    OBJECTIVE RD SHARMA|Exercise Exercise|72 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    OBJECTIVE RD SHARMA|Exercise Section I - Solved Mcqs|71 Videos

  • INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Illustration|1 Videos

  • LIMITS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|60 Videos

Similar Questions

Explore conceptually related problems

2 tan ^(-1)x-log(1+x^(2))

log_(e)sin^(-1)x^(2)(cot^(-1)x^(2))

Knowledge Check

  • If y=tan^(-1)[(log(e//x^(3)))/(log(ex^(3)))]+tan^(-1)[(log(e^(4)x^(3)))/(log(e//x^(12)))]," then "(d^(2)y)/(dx^(2))=

    A
    `-1`
    B
    0
    C
    1
    D
    `(-2x)/((1+x^(2))^(2))`

  • If y=tan^(-1)((log ex^(-2))/(log ex^(2)))+tan^(-1)((3+2log x)/(1-6log x)) then (d^(2)y)/(dx^(2)) is

    A
    2
    B
    1
    C
    0
    D
    x

  • If f(x)=tan^(-1)((ln(e//x^(3)))/(ln (ex^(3))))+tan^(-1)(ln(e^(4)x^(3))/(ln(e//x^(12))))(AA x ge e) incorrect statement is

    A
    `f(x)` is a constant function
    B
    `f(x) ge0`
    C
    `f(x)` is an even function
    D
    `f(x) gepi`

    • Similar Questions

    Explore conceptually related problems

    (d)/(dx)[(tan^(-1)(log((e)/(x^(2)))))/(log(ex^(2)))]=

    int(e^(ln tan^(-1)x))/(1+x^(2))dx

    f(x)=tan^(-1){(log((e)/(x^(2))))/(log(ex^(2)))}+tan^(-1)((3+2log x)/(1-6log x)) then find (d^(n)y)/(dx^(n))

    If 2tan^(- 1)(c o s e c(tan^(- 1)(x))-tan(cot^(- 1)(x)))=tan^(- 1)y then y is equal to

    If quad y=tan^(-1){(log_(e)((e)/(x^(2))))/(log_(e)(ex^(2)))}+tan^(-1)((3+2log_(e)x)/(1-6log_(e)x)), then (d^(2)y)/(dx^(2))=

    Home
    Profile