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The value of (sin frac(pi)(8) + i cos fr...

The value of `(sin frac(pi)(8) + i cos frac(pi)(8))^(8)/((sin frac(pi)(8) - i cos frac(pi)(8))^(8))` is :

A

`-1`

B

0

C

1

D

`2i`

Text Solution

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The correct Answer is:
C
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((sin((pi)/(8))+i cos((pi)/(8)))^(8))/((sin((pi)/(8))-i cos((pi)/(8)))^(8)) =

The expression [(1+sin((pi)/(8))+i cos((pi)/(8)))/(1+sin((pi)/(8))-i cos((pi)/(8)))]^(8)

Knowledge Check

  • [(1 + sin "" (pi)/( 8) + i cos "" (pi)/( 8))/( 1 + sin "" (pi)/( 8) - i cos "" (pi)/( 8))]^(8) =

    A
    `-1`
    B
    `1`
    C
    `i`
    D
    `-i`

  • The smallest positive integral value of n such that [(1 + sin ""(pi)/(8) + i cos"" (pi)/(8))/(1 + sin "" (pi)/(8) - i cos "" (pi)/(8))] is purely imaginary is

    A
    2
    B
    3
    C
    4
    D
    1

  • (frac(-1)(5))^(3) div (frac(-1)(5))^(8)= ?

    A
    (a) `(-frac(1)(5))^(5)`
    B
    (b) `(frac(-1)(5))^(11)`
    C
    (c) `(-5)^(5)`
    D
    (d) `(frac(1)(5))^(5)`

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    Find the value of (a) sin(pi)/(8) (b) cos(pi)/(8) (c) tan (pi)/(8)

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