What is the value of arctan(cot(pi/8)) ?

The value of arctan(cot(pi/8)) is (3pi)/8

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arctan(cot(pi/8))

arctan (cot (\frac{π}{8}))

\frac{3 π}{8}

Decimal Notation

67.5

Solution steps

arctan (cot (\frac{π}{8}))

Rewrite using trig identities:

cot (\frac{π}{8}) = tan (\frac{3 π}{8})

cot (\frac{π}{8})

tan (\frac{π}{2} - x) = cot (x)

= tan (\frac{π}{2} - \frac{π}{8})

= tan (\frac{3 π}{8})

= arctan (tan (\frac{3 π}{8}))

Use the inverse trig property:

\frac{3 π}{8}

arctan (tan (\frac{3 π}{8}))

For

- \frac{π}{2} < x < \frac{π}{2}, a rc t an (t an (x)) = x

- \frac{π}{2} < \frac{3 π}{8} < \frac{π}{2}

= \frac{3 π}{8}

= \frac{3 π}{8}

arctan (\frac{20}{30})

7 cos (\frac{π}{6})

sin^{2} (1) + cos^{2} (1)

30 sin (2 5^{\circ})

4 cos (4 5^{\circ}) - 2 sin (4 5^{\circ})

What is the value of arctan(cot(pi/8)) ?
The value of arctan(cot(pi/8)) is (3pi)/8