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The expression [(1+sin(pi/8)+icos(pi/8))...

The expression `[(1+sin(pi/8)+icos(pi/8))/(1+sin(pi/8)-icos(pi/8))]^8` is equal is

A

1

B

`-1`

C

i

D

`-i`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `sin""(pi)/(8)+icos""(pi)/(8)=z`
`rArr [(1+sin""(pi)/(8)+icos""(pi)/(8))/(1+sin""(pi)/(8)-icos""(pi)/(8))]^(8)`
`=((1+z)/(1+(1)/(z)))^(8)=z^(8)`
`=(sin""(pi)/(8)+icos""(pi)/(8))^(8)`
`=(cos""((pi)/(2)-(pi)/8)+isin""((pi)/(2)-(pi)/(8)))^(8)`
`=(cos""(3pi)/(8)+isin""(3pi)/(8))^(8)=cos3pi=-1`
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