What is the value of sec(arcsin(40/41)) ?

The value of sec(arcsin(40/41)) is 41/9

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sec(arcsin(40/41))

sec (arcsin (\frac{40}{41}))

\frac{41}{9}

Decimal

4.55555 \dots

Solution steps

sec (arcsin (\frac{40}{41}))

Rewrite using trig identities:

sec (arcsin (\frac{40}{41})) = \frac{1 - ( \frac{40}{41} ) ^{2}}{1 - ( \frac{40}{41} ) ^{2}}

Use the following identity:

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

= \frac{1 - ( \frac{40}{41} ) ^{2}}{1 - ( \frac{40}{41} ) ^{2}}

= \frac{1 - ( \frac{40}{41} ) ^{2}}{1 - ( \frac{40}{41} ) ^{2}}

Simplify

= \frac{41}{9}

What is the value of sec(arcsin(40/41)) ?
The value of sec(arcsin(40/41)) is 41/9