What is the value of csc(arcsec((sqrt(6))/2)) ?

The value of csc(arcsec((sqrt(6))/2)) is square root of 3

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csc(arcsec((sqrt(6))/2))

csc (arcsec (\frac{6}{2}))

3

Decimal Notation

1.73205 \dots

Solution steps

csc (arcsec (\frac{6}{2}))

Rewrite using trig identities:

csc (arcsec (\frac{6}{2})) = \frac{1}{1 - \frac{1}{( \frac{6}{2} ) ^{2}}}

Use the following identity:

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

= \frac{1}{1 - \frac{1}{( \frac{6}{2} ) ^{2}}}

= \frac{1}{1 - \frac{1}{( \frac{6}{2} ) ^{2}}}

Simplify

= 3

\frac{cos ( 14 0 ^{\circ} ) - cos ( 10 0 ^{\circ} )}{sin ( 14 0 ^{\circ} ) - sin ( 10 0 ^{\circ} )}

sin (sin (\frac{π}{2}))

67 sin (5 0^{\circ})

e^{\frac{π}{2}} - e^{a r c t a n (1 + (0)^{2})}

\frac{sin ( 2 0 ^{\circ} )}{cos ( 2 0 ^{\circ} )}

What is the value of csc(arcsec((sqrt(6))/2)) ?
The value of csc(arcsec((sqrt(6))/2)) is square root of 3