How do you find $cos ({cot}^{- 1} \sqrt{3})$ $cos( cot^{-1} sqrt{3} )$ without a calculator?

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Answer 1 · 2018-06-14T03:15:46

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${cot}^{- 1} \sqrt{3} = \frac{1}{{tan}^{- 1} \sqrt{3}} = \frac{1}{60}$ $cot^(-1)sqrt3 = 1/tan^(-1)sqrt3 = 1/60$

Since $\frac{1}{60}$ $1/60$ is approximately equal to $0.010$ $0.010$ and looking at the $y = cos x$ $y=cosx$ graph below,

graph{cosx [-10, 10, -5, 5]}

We can give an approximation that $cos (\frac{1}{60}) = 1$ $cos (1/60)=1$

How do you find cos( cot^{-1} sqrt{3} )cos(cot−1√3)cos( cot^{-1} sqrt{3} ) without a calculator?