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If number of solution and sum of solution of the equation ` 3sin^(2)x-7sinx +2=0, x in [0,2pi]` are respectively N and S and ` f_(n)(theta)=sin^(n)theta +cos^(n) theta`. On the basis of above information , answer the following questions.
Value of N is

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
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Knowledge Check

  • If number of solution and sum of solution of the equation 3sin^(2)x-7sinx +2=0, x in [0,2pi] are respectively N and S and f_(n)(theta)=sin^(n)theta +cos^(n) theta . On the basis of above information , answer the following questions. If alpha is solution of equation 3sin^(2)x-7sinx+2=0, x in [0,2pi] , then the value of f_(4)(alpha) is

    A
    `(97)/(81)`
    B
    `(57)/(81)`
    C
    `(65)/(81)`
    D
    0

  • If 3sin^(2)x-7sin x +2=0, x in [0(pi)/(2)] and f_(n)(theta)=sin^(n) theta + cos^(n) theta . On the basis of above information , answer the questions The value of ( sin 5 x + sin 4 x)/( 1+ 2 cos 3 x) is

    A
    `(3+ 2 sqrt(2))/(9)`
    B
    `(3+ 4sqrt(2))/(9)`
    C
    `(4sqrt(2)-2)/(9)`
    D
    `(4sqrt(2)-3)/(9)`

  • If 3sin^(2)x-7sin x +2=0, x in [0(pi)/(2)] and f_(n)(theta)=sin^(n) theta + cos^(n) theta . On the basis of above information , answer the questions The value of f_(4)(x) is

    A
    `(97)/(81)`
    B
    `(57)/(81)`
    C
    `(65)/(81)`
    D
    `(73)/(81)`

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