Question

cot[cos^−1(−1/2) + cos^−1(1/2) + tan^−1(1/3)]

Answer 1

\[\cos^{-1}(-\frac{1}{2})=120\]
\[\cos^{-1}(\frac{1}{2})=60\]
\[\tan^{-1}(\frac{1}{3})\] is a mystery to me but so far we have
\[\cos(180+\tan^{-1}(\frac{1}{3}))\]

Answer 2

now \(\cos(180+x)=-\cos(x)\) so your final job is to find \[-\cos(\tan^{-1}(\frac{1}{3}))\] which is identical to saying "if the tangent is 1/3, what is the cosine?
you can do that by drawing a triangle

Answer 3

there is a picture of an angle whose tangent is \(\frac{1}{3}\)
by pythagoras the hypotenuse is \(\sqrt{10}\) so the cosine of that angle is
\[\frac{3}{\sqrt{10}}\] and so your answer is
\[-\frac{3}{\sqrt{10}}\]

Answer 4

That makes so much sense, thank you for explaining it to me step by step! :)

Answer 5

yw