If tan(cos-1 x) = sin(cot-1 1/2) then x is equal to

(a) 1/√5

(b) 2/√5

(c) 3/√5

(d) √5/3

Solution:

Given tan(cos-1 x) = sin(cot-1 1/2)

Let cot-1 ½ = θ

Then sin θ = 2/√5

Let cos-1 x = β

=> x = cos β

tan β = √(1-x2)/x = 2/√5

=> (1-x2)/x2 = 4/5

=> 5-5x2 = 4x2

=> 9x2 = 5

=> x = √5/3

Hence option d is the answer.

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