What is the value of sec(arctan(6/7)) ?

The value of sec(arctan(6/7)) is (sqrt(85))/7

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sec(arctan(6/7))

sec (arctan (\frac{6}{7}))

\frac{85}{7}

Decimal Notation

1.31707 \dots

Solution steps

sec (arctan (\frac{6}{7}))

Rewrite using trig identities:

sec (arctan (\frac{6}{7})) = 1 + (\frac{6}{7})^{2}

Use the following identity:

sec (arctan (x)) = 1 + x^{2}

= 1 + (\frac{6}{7})^{2}

= 1 + (\frac{6}{7})^{2}

Simplify

= \frac{85}{7}

- cos (4 π)

sin (\frac{π}{3}) cos (\frac{π}{7}) - sin (\frac{π}{7}) cos (\frac{π}{3})

4 sec^{2} (0)

csc (\frac{- 5 π}{6})

2 tan (3 0^{\circ})

What is the value of sec(arctan(6/7)) ?
The value of sec(arctan(6/7)) is (sqrt(85))/7