What is the value of csc(arcsec(-2sqrt(5))) ?

The value of csc(arcsec(-2sqrt(5))) is (2sqrt(95))/(19)

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csc(arcsec(-2sqrt(5)))

csc (arcsec (- 25))

\frac{2 95}{19}

Decimal

1.02597 \dots

Solution steps

csc (arcsec (- 25))

Rewrite using trig identities:

csc (arcsec (- 25)) = \frac{1}{1 - \frac{1}{( - 2 5 ) ^{2}}}

Use the following identity:

csc (arcsec (x)) = \frac{1}{1 - \frac{1}{x ^{2}}}

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

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

Simplify

= \frac{2 95}{19}

What is the value of csc(arcsec(-2sqrt(5))) ?
The value of csc(arcsec(-2sqrt(5))) is (2sqrt(95))/(19)