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Find cos 2x if tan x=1/\(\sqrt{3}\).(a) 1/2(b) 0(c) \(\sqrt{3}\)/2(d) 1This question was posed to me in an internship interview.The question is from Trigonometric Functions of Sum and Difference of Two Angles-1 in chapter Trigonometric Functions of Mathematics – Class 11

Answer»

Right answer is (a) 1/2

Easy explanation: We know, COS 2X = cos^2x – sin^2x = (cos^2x – sin^2x)/(cos^2x+sin^2x) {1 = sin^2x + cos^2x}

= (1-tan^2x)/(1+tan^2x)

= (1-(1/\(\sqrt{3}\))^2)/(1+(1/\(\sqrt{3}\))^2)

= (1-1/3)/(1+1/3) = (2/3)/(4/3) = 1/2.


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