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

The value of tan(arcsec(-2sqrt(5))) is -sqrt(19)

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tan(arcsec(-2sqrt(5)))

tan (arcsec (- 25))

- 19

Decimal Notation

- 4.35889 \dots

Solution steps

tan (arcsec (- 25))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= - 19

sin (\frac{- 13 π}{6})

cos (arcsin (- \frac{1}{5}))

cosh (ln (2)) + sinh (ln (2))

18 0^{\circ} - arcsin (\frac{182 sin ( 4 0 ^{\circ} )}{255})

5 \cdot sin (2 5^{\circ})

What is the value of tan(arcsec(-2sqrt(5))) ?
The value of tan(arcsec(-2sqrt(5))) is -sqrt(19)