If ecos x - e-cos x = 4, then the value of cos x is

1) log(2 + √5)

2) – log(2 + √5)

3) log( – 2 + √5)

4) None of the above

Solution: (4) None of the above

ecos x – e-cos x = 4

Put ecosx = t

t – (1 / t) = 4

t2 – 4t – 1 = 0

t = [4 ± √42 + 4] / 2

= [2 ± √22 + 1]

= 2 ± √5

ecos x = 2 + √5

cos x = lne (2 + √5)

e = 2.71

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