Home
Class 12
MATHS
Statement I sin x=a , where -1 lt a lt...

Statement I `sin x=a , ` where `-1 lt a lt 0 `, then for ` x in [0,npi]` has `2(n-1) ` solution ` AA n in N` .
Statement II sin x takes value a exactly two times when we take one complete rotation covering all the quadrants starting from x=0 .

A

Statement I is true , Statement II is true , Statement II is a correct explanation for Statement I.

B

Statement I is true , Statement II is true , Statement II is not a correct explanation for Statement II.

C

Statement I is true , Statement II is false

D

Statement I is false , Statement II true .

Text Solution

Verified by Experts

The correct Answer is:
d
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    ARIHANT MATHS|Exercise Exercise (Matching Type Questions)|2 Videos

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|23 Videos

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|12 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|44 Videos

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|19 Videos

Similar Questions

Explore conceptually related problems

If tan x = 1, 0 lt x lt 90^(@) , then what is the value of 2 sin x cos x?

Statement 1: If is a sequence such that a_(1)=1 and a_(n+1)=sin a_(n), then lim_(n rarr oo)a_(n)=0. Statement 2:sin cex>sin x AA x>0

Knowledge Check

  • If -1 lt x lt 0 then sin^(-1) x equals-

    A
    `pi- cos^(-1) (sqrt(1-x^(2)))`
    B
    `tan^(-1) ((x)/(sqrt(1-x^(2))))`
    C
    `-cos^(-1)((sqrt(1-x^(2)))/(x))`
    D
    `cosec^(-1)x`

  • Statement I The number of solution of the equation |sin x|=|x| is only one. Statement II |sin x| ge 0 AA x in R .

    A
    Statement I is true , Statement II is true , Statement II is a correct explanation for Statement I.
    B
    Statement I is true , Statement II is true , Statement II is not a correct explanation for Statement II.
    C
    Statement I is true , Statement II is false
    D
    Statement I is false , Statement II true .

  • Statement I : If -1 le x lt 0 , then cos (sin^(-1)x) = -sqrt(1-x^(2)) Statement II : If -1 le x lt 0 , then sin (cos^(-1)x) = sqrt(1 - x^(2)) Which one of the following is correct is respect of the above statements ?

    A
    Both statement I and II are independently correct and statement II is the correct explanation of statement I
    B
    Both statements I and II are independently correct but statement II is not the correct explanation of statement I
    C
    Statement I is correct but statement II is false
    D
    Statement I is false but statement II is correct.

    • Similar Questions

    Explore conceptually related problems

    If sqrt(3) sin x - cos x = 0 and 0 lt x lt 90 , find the value of x .

    sin2x + cos 2x + sin x + cos x + 1 = 0 has no solution in the first quadrant.

    Statement-2 f(x)=(sin x)/(x) lt 1 for lt x lt pi/2 Statement -2 f(x)=(sin x)/(x) is decreasing function on (0,pi//2)

    If sin x - cos x = 0, 0^(@) lt x lt 90^(@) then the value of ( sec x + cosec x)^(2) is:

    Let y= sin^(-1)"" (2 x)/(1 +x^2) where 0 lt x lt 1 and 0 lt y lt pi/2 then ( dy)/(dx) is equal to

    Home
    Profile