## anonymous 3 years ago cot[cos^−1(−1/2) + cos^−1(1/2) + tan^−1(1/3)]

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1. anonymous

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

2. anonymous

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

3. anonymous

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4. anonymous

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 $-\frac{3}{\sqrt{10}}$

5. anonymous

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

6. anonymous

yw