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STATEMENT -1 : tan^(-1)x=sin^(-1)yrArry ...

STATEMENT -1 : `tan^(-1)x=sin^(-1)yrArry in (-1,1)`
and
STATEMENT -2 : `-pi/2 lt tan^(-1)x lt pi/2`

A

Statement -1 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

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The correct Answer is:
A
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sin^(-1)x+tan^(-1)x=(pi)/(2)

STATEMENT-1 : If tan^2 (sin^-1x) > 1 then x in(-1-1/sqrt2)uu(1/sqrt(2).1).STATEMENT-2 : The number of positive integral solution of tan^-1 1/y+cot^-1(1/x)=cot^-1(1/3), where x/y < 1, is 2. STATEMENT -3 : If sin^-1 x=-cos^-1 sqrt(1-x^2) and sin^-1 y=cos^-1 sqrt(1-y^2), then the exact range of (tan^-1 x+ tan6-1 y) is [-pi/4,pi/4].

Knowledge Check

  • STATEMENT -1 : The value of tan^(-1)x+tan^(-1)(1/x)=pi/2, AA x in R -{0} . and STATEMENT -2 : The value of tan^(-1).(1/x)={:{(cot^(-1)x,x gt0),(-pi+cot^(-1)x,x lt0):}

    A
    Statement -1 is True, Statement-2 is True, Statement -2 is a correct explanation for Statement -4
    B
    Statement -1 is True, Statement -2 is True, Statement -2 is NOT a correct explanation for Statement -4
    C
    Statement-1 is True, Statement -2 is False
    D
    Statement -1 is False, Statement -2 is True

  • If tan^(-1) x+tan^(-1) ""1/2 = pi/4 , " then " x=

    A
    `-3`
    B
    3
    C
    2
    D
    `1//3`

  • The values of x which satisfy 18(sin^(-1)x)^(2)-9pi sin^(-1)x +pi^(2)lt 0 and 18(tan^(-1)x)^(2)-9pi tan^(-1)x + pi^(2)lt 0 simultaneously are

    A
    `((sqrt(3))/(3),(sqrt(3))/(2))`
    B
    `((sqrt(3))/(2),1)`
    C
    `((1)/(3),(sqrt(3))/(2))`
    D
    `((1)/(sqrt(3)),sqrt(3))`

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