Home
Class 12
MATHS
If cos^(-1)(cosx)=sqrt(1sin2x)AAxepsi(0,...

If `cos^(-1)(cosx)=sqrt(1sin2x)AAxepsi(0,2pi),` then no. of solution =

A

2

B

4

C

3

D

5

Text Solution

Verified by Experts

The correct Answer is:
A

`sqrt(sin2x)=|sin x+ cos x|`
`=sqrt(2)|sin(x+(pi)/(4))|`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • MOCK TEST 4

    CAREER POINT|Exercise MATHS|30 Videos

  • MOCK TEST 6

    CAREER POINT|Exercise Part (C) (MATHS)|30 Videos

Similar Questions

Explore conceptually related problems

Solve cos^(-1)(cosx)>sin^(-1)(sinx),x in [0,2pi]

If sqrt(3) ( cos^2 x) = ( sqrt(3)-1) cos x +1, the numbers of solution of the given equation when x in [0,pi/2] is

Knowledge Check

  • int(cos2x)/((e^(-x)+cosx)sqrt(1+sin2x))dx,x in(0,(pi)/(2)) is equal to

    A
    `log_(e)|1+e^(x)sinx|+c`
    B
    `log_(e)|e^(x)+cosx|+c`
    C
    `log_(e)|1+e^(x)cosx|-x+c`
    D
    `log_(e)|1+e^(x)cosx|+c`

  • sqrt(cos 2x)+sqrt(1+sin2x)=2sqrt(sinx+cosx) if

    A
    `sin x+cosx=1 `
    B
    `x =2n pi `
    C
    `x=n pi+pi//4 `
    D
    `sin x -cosx=0`

  • If (sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))=cot(a+x/2) and x in (pi,2pi) then 'a' is equal to :

    A
    `(pi)/4`
    B
    `(pi)/2`
    C
    `(pi)/3`
    D
    None of these

    • Similar Questions

    Explore conceptually related problems

    Number of solutions of the equation cos ec^(-1)(cos ecx)=sin x. in [-2 pi,2 pi] is 'a' and number of solutions of cos ec^(-1)(cos ecx)=sqrt(sin x) in this interval is 'b' then sqrt(a+b) is

    If x in[0,2 pi] for which 2cos x<=|sqrt(1+sin2x)-sqrt(1-sin2x)|<=sqrt(2) has solution set x in[(lambda pi)/(4),(mu pi)/(4)] then value of lambda+mu is

    If 2cosx(4sin(pi/4+x) sin(pi/4-x)-1)=1 then for x in [0,pi] then the number of solution s is n ,and the sum of solutions is s then find the value of (n,s)

    Consider the function f(x)=(sqrt(1+cos x)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cos x)) then Q. If x in (pi, 2pi) then f(x) is

    The total number of solutions of cos x= sqrt(1- sin 2x) in [0, 2pi] is equal to

    Home
    Profile