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

The value of sec(arcsin((sqrt(2))/5)) is (5sqrt(23))/(23)

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

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

\frac{5 23}{23}

Decimal Notation

1.04257 \dots

Solution steps

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

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{5 23}{23}

4 cos^{2} (16 5^{\circ}) - 2

sin (3 0^{\circ}) + sin (12 0^{\circ}) + cos (24 0^{\circ}) - cos (33 0^{\circ})

arctan (sin (\frac{11 π}{4}))

cos (54. 7^{\circ})

8 (cos (\frac{7 π}{4}) + i sin (\frac{7 π}{4}))

What is the value of sec(arcsin((sqrt(2))/5)) ?
The value of sec(arcsin((sqrt(2))/5)) is (5sqrt(23))/(23)