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If e^(cos x) -e^(-cos x) = 4, then the v...

If `e^(cos x) -e^(-cos x) = 4`, then the value of cos x, is

A

`log (2+sqrt(5))`

B

`-log(2+sqrt(5))`

C

`log(-2+sqrt(5))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
D
Put `e^(cos x) = t` then `t - 1/t = 4`
`rArr t^(2) - 4t - 1 = 0 rArr t = (+4-sqrt(16+4))/(2)`
`rArr t = (4+- sqrt(20))/(2) = 2 +- sqrt(5)`
`e^(cosx) = 2 - sqrt(5) , e^(cosx) = 2+sqrt(5) rarr "Not possible"`
can't negative , `e^(cosx) le 2.7` because `cos x le 1`
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