What is the value of cot(arcsin(1/(sqrt(7)))) ?

The value of cot(arcsin(1/(sqrt(7)))) is square root of 6

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cot(arcsin(1/(sqrt(7))))

cot (arcsin (\frac{1}{7}))

6

Decimal Notation

2.44948 \dots

Solution steps

cot (arcsin (\frac{1}{7}))

Rewrite using trig identities:

cot (arcsin (\frac{1}{7})) = \frac{1 - ( \frac{1}{7} ) ^{2}}{( \frac{1}{7} )}

Use the following identity:

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

= \frac{1 - ( \frac{1}{7} ) ^{2}}{( \frac{1}{7} )}

= \frac{1 - ( \frac{1}{7} ) ^{2}}{\frac{1}{7}}

Simplify

= 6

tan (arccos (- \frac{1}{3}))

5 cos (16 0^{\circ})

\frac{1}{4} sin (\frac{π}{2})

- \frac{2 cos ( π )}{2 - 4 sin ( π )}

tan (\frac{12}{9})

What is the value of cot(arcsin(1/(sqrt(7)))) ?
The value of cot(arcsin(1/(sqrt(7)))) is square root of 6