What is the value of sec(arctan(9/10)) ?

The value of sec(arctan(9/10)) is (sqrt(181))/(10)

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sec(arctan(9/10))

sec (arctan (\frac{9}{10}))

\frac{181}{10}

Decimal Notation

1.34536 \dots

Solution steps

sec (arctan (\frac{9}{10}))

Rewrite using trig identities:

sec (arctan (\frac{9}{10})) = 1 + (\frac{9}{10})^{2}

Use the following identity:

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

= 1 + (\frac{9}{10})^{2}

= 1 + (\frac{9}{10})^{2}

Simplify

= \frac{181}{10}

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What is the value of sec(arctan(9/10)) ?
The value of sec(arctan(9/10)) is (sqrt(181))/(10)