Answer:
2√5
cos x = -------------
5
Explanation:
If tan x = 1/2 then what is cos x?
Recall that tan x is defined as the quotient sin x / cos x, so that in this case sin x / cos x = 1 / 2 = opp side / adjacent side. Also, recall that cos x = adj side / hypotenuse.
To determine cos x, we need to find the length of the hypotenuse. That, in turn, through use of the Pythagorean Theorem, is √(1^2+2^2), or √5.
Then cos x = adj side / hyp = 2/√5. Rationalizing the denominator, we get
2√5
cos x = -------------
5