What is the value of sec(arcsin((2sqrt(5))/5)) ?

The value of sec(arcsin((2sqrt(5))/5)) is square root of 5

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sec(arcsin((2sqrt(5))/5))

sec (arcsin (\frac{2 5}{5}))

5

Decimal Notation

2.23606 \dots

Solution steps

sec (arcsin (\frac{2 5}{5}))

Rewrite using trig identities:

sec (arcsin (\frac{2 5}{5})) = \frac{1 - ( \frac{2 5}{5} ) ^{2}}{1 - ( \frac{2 5}{5} ) ^{2}}

Use the following identity:

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

= \frac{1 - ( \frac{2 5}{5} ) ^{2}}{1 - ( \frac{2 5}{5} ) ^{2}}

= \frac{1 - ( \frac{2 5}{5} ) ^{2}}{1 - ( \frac{2 5}{5} ) ^{2}}

Simplify

= 5

sin (3 5^{\circ}) cos (1 0^{\circ}) + cos (3 5^{\circ}) sin (1 0^{\circ})

- sin^{2} (0)

250 cos (3 0^{\circ})

arctan (\frac{36}{28})

2 cos^{2} (\frac{π}{6}) - 1

What is the value of sec(arcsin((2sqrt(5))/5)) ?
The value of sec(arcsin((2sqrt(5))/5)) is square root of 5