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

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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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