How do you solve and find the value of cos(tan^-1sqrt3)?

1 Answer
Alan P.
Dec 27, 2016

cos(tan^(-1)(sqrt(3)))=color(green)(1/2)

Explanation:

The standard definition of the inverse tan function implies an angle either Quadrant I or II.

The angle theta=tan^(-1)(sqrt(3)) can be represented by means of a right triangle in standard position with opposite side of length sqrt(3) and adjacent side of length 1.
By the Pythagorean Theorem this implies a hypotenuse of sqrt((sqrt(3)^2+1^2))=sqrt(4)=2

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Using this triangle and the definition of cos as "adjacent"/"hypotenuse"
we have
color(white)("XXX")cos(tan^(-1)(sqrt(3)))=1/2

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