How do you solve and find the value of cos(tan^-1sqrt3)cos(tan−1√3)?

1 Answer
Alan P.
Dec 27, 2016

cos(tan^(-1)(sqrt(3)))=color(green)(1/2)cos(tan−1(√3))=12

Explanation:

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

The angle theta=tan^(-1)(sqrt(3))θ=tan−1(√3) can be represented by means of a right triangle in standard position with opposite side of length sqrt(3)√3 and adjacent side of length 11.
By the Pythagorean Theorem this implies a hypotenuse of sqrt((sqrt(3)^2+1^2))=sqrt(4)=2√(√32+12)=√4=2

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Using this triangle and the definition of coscos as "adjacent"/"hypotenuse"adjacenthypotenuse
we have
color(white)("XXX")cos(tan^(-1)(sqrt(3)))=1/2XXXcos(tan−1(√3))=12

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