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If (x)/(cos theta)=(y)/(cos(theta-(2pi)/...

If `(x)/(cos theta)=(y)/(cos(theta-(2pi)/(3)))=(z)/(cos(theta+(2pi)/(3))), then x+y+z=`

A

1

B

0

C

`-1`

D

none of these.

Text Solution

Verified by Experts

The correct Answer is:
B
We have
`(x)/(cos theta)=(y)/(cos(theta-(2pi)/(3)))=(1)/(cos(theta+(2pi)/(3)))`
Therefore each ratio is equal to
`(x+y+z)/(cos theta+cos(theta-(2pi)/(3)))=(x)/(cos(theta+(2pi)/(3)))=(x+y+z)/(0)`
or `x+y+z=0`
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