What is the value of cos(arccsc(-sqrt(2))) ?

The value of cos(arccsc(-sqrt(2))) is sqrt(1/2)

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cos(arccsc(-sqrt(2)))

cos (arccsc (- 2))

\frac{1}{2}

Decimal Notation

0.70710 \dots

Solution steps

cos (arccsc (- 2))

Rewrite using trig identities:

cos (arccsc (- 2)) = \frac{( - 2 ) ^{2} - 1}{( - 2 ) ^{2}}

Use the following identity:

cos (arccsc (x)) = \frac{x ^{2} - 1}{x ^{2}}

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

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

Simplify

= \frac{1}{2}

9 tan (7 5^{\circ})

sin (2 π - \frac{π}{3})

\frac{tan ( 2 4 ^{\circ} )}{98}

csc (2 6^{\circ})

\frac{3}{sin ( 4 0 ^{\circ} )}

What is the value of cos(arccsc(-sqrt(2))) ?
The value of cos(arccsc(-sqrt(2))) is sqrt(1/2)