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For the smallest positive values of x an...

For the smallest positive values of x and y, the eqation `2 (sin x + sin y) - 2 cos ( x - y) = 3` has a solution, then which of the following is/are true ?

A

`"sin"(x+y)/2=1`

B

`cos((x-h)/2)=1/2`

C

number of ordered pairs (x,y) is 2

D

number of ordered pairs (x,y) is 3

Text Solution

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The correct Answer is:
A, B, C
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Knowledge Check

  • The smallest positive real value of p for which the equation cos (p sin x) = sin (p cos x) has a solution where x in [0, 2pi] is

    A
    `(pi sqrt(2))/(4)`
    B
    `(pi)/(4)`
    C
    `(pi)/(2)`
    D
    `(sqrt(3)pi)/(4)`

  • The smallest positive values of x and y which satisfy tan (x-y)=1, sec (x+y)=2//sqrt(3) are

    A
    `x = (25pi)/(24), y = (19pi)/(24)`
    B
    `x=(7pi)/(24), y = (37 pi)/(24)`
    C
    `x = (pi)/(4), y = (pi)/(2)`
    D
    `x = (pi)/(3), y = (7pi)/(12)`

  • The range of y such that the equation in x , y cos x = sin x has a real solution is

    A
    [-2,2]
    B
    `[-sqrt(2), sqrt(2)]`
    C
    [-1,1]
    D
    `[-1//2, 1//2]`

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