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If Cos20^0=k and Cosx=2k^2-1, then the p...

If `Cos20^0=k` and `Cosx=2k^2-1`, then the possible values of x between `0^0 and 360^0` are

A

`140^(@)and270^(@)`

B

`40^(@)and140^(@)`

C

`40^(@)and320^(@)`

D

`50^(@)and130^(@)`

Text Solution

Verified by Experts

The correct Answer is:
C
Given , `k=cos20^(@)`
`2k^(2)-1=cosx`
`therefore2cos^(2)20^(@)-1=cosx`
`rArrcosx=cos40^(@)rArrx=40^(@)`
or `x=360^(@)-40^(@)=320^(@)`
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