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If f(n)(x) = (sin x)/(cos3x)+(sin 3x)/(c...

If `f_(n)(x) = (sin x)/(cos3x)+(sin 3x)/(cos 3^(2)x) +(sin 3^(2)x)/(cos 3^(3)x) +....+ (sin 3^(n-1)x)/(cos 3^(n)x)"Then" f_(2) ((pi)/(4)) + f_(3) ((pi)/(4))=`

A

0

B

1

C

-1

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • If f_(n)(x)=(sinx)/(cos3x)+(sin3^2x)/(cos3^2x)+(sin3^2x)/(cos3^(3)x)+....+(sin3^(n-1)x)/(cos3^(n)x) Then f_(2)(pi//4)+f_3(pi//4)=

    A
    0
    B
    1
    C
    `-1`
    D
    2

  • int (a cos^(3)x+b sin^(3)x)/(cos^(2)x sin^(2)x)dx=

    A
    `a"cosec" x+b sec x+c`
    B
    `-a "cosex" x+b sec x+c`
    C
    `-a "cosec"x-b sec x+ c`
    D
    `a-"cosec"x+a secx+c`

  • int (3 cos 3x-2 sin 2x)/(cos 2x+ sin 3x)dx=

    A
    `-log |cos 2x-sin 3x|+c`
    B
    `log |cos 2x-sin 3x|+c`
    C
    `log |cos 2x+sin 3x|+c`
    D
    none

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    If f(x) = (cos x + i sin x)(cos 3x + i sin 3x) ….(cos (2n - 1)x + i(sin(2n - 1)x) , then f^(11)(x) is

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