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The equation sinx(sinx+cosx)=k has real ...

The equation `sinx(sinx+cosx)=k` has real solutions, where k is a real number, Then

A

`0lekle(1+sqrt2)/(2)`

B

`2-sqrt3lekle2+sqrt3`

C

`0lekle2-sqrt3`

D

`(1-sqrt2)/(2)lekle(1+sqrt2)/(2)`

Text Solution

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The correct Answer is:
D
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Knowledge Check

  • The equation sinx=[1+sinx]+[1-cosx] has [where [.] is greatest integer function]

    A
    no solution in `[-pi/2, pi/2]`
    B
    no solution in `[pi/2, pi]`
    C
    no solution in `[pi, (3pi)/2]`
    D
    no solution for `x in -[pi/2, (3pi)/2]`

  • The equation a cos theta + b sin theta =c has a solution when a, b anc c are real numbers such that-

    A
    `a lt b lt c`
    B
    `a=b =c`
    C
    `c^(2)lt a^(2) -b^(2)`
    D
    `c ^(2) le a^(2) +b^(2)`

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