What is cot(arcsin(1/v)) ?

The solution to cot(arcsin(1/v)) is sqrt(v^2-1)

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simplify cot(arcsin(1/v))

simplify

cot (arcsin (\frac{1}{v}))

v^{2} - 1

Solution steps

cot (arcsin (\frac{1}{v}))

Use the following identity:

cot (arcsin (x)) = \frac{1 - x ^{2}}{x}

= \frac{1 - ( \frac{1}{v} ) ^{2}}{( \frac{1}{v} )}

Simplify

= v^{2} - 1

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