What is the value of sec(arctan((sqrt(3))/3)) ?

The value of sec(arctan((sqrt(3))/3)) is (2sqrt(3))/3

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sec(arctan((sqrt(3))/3))

sec (arctan (\frac{3}{3}))

\frac{2 3}{3}

Decimal Notation

1.15470 \dots

Solution steps

sec (arctan (\frac{3}{3}))

Rewrite using trig identities:

sec (arctan (\frac{3}{3})) = 1 + (\frac{3}{3})^{2}

Use the following identity:

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

= 1 + (\frac{3}{3})^{2}

= 1 + (\frac{3}{3})^{2}

Simplify

= \frac{2 3}{3}

arctan (tan (\frac{5 π}{6}))

csc (- \frac{3 π}{2})

cos^{3} (\frac{π}{4})

- sin (2)

sin (\frac{- 4 π}{3})

What is the value of sec(arctan((sqrt(3))/3)) ?
The value of sec(arctan((sqrt(3))/3)) is (2sqrt(3))/3