What is the value of cos(arctan(-sqrt(3)))+csc(arcsec(2)) ?

The value of cos(arctan(-sqrt(3)))+csc(arcsec(2)) is 1/2+(2sqrt(3))/3

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cos(arctan(-sqrt(3)))+csc(arcsec(2))

cos (arctan (- 3)) + csc (arcsec (2))

\frac{1}{2} + \frac{2 3}{3}

Solution steps

cos (arctan (- 3)) + csc (arcsec (2))

Rewrite using trig identities:

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

= cos (arctan (- 3)) + \frac{1}{1 - \frac{1}{2 ^{2}}}

Simplify

= cos (arctan (- 3)) + \frac{2 3}{3}

Rewrite using trig identities:

cos (arctan (- 3)) = \frac{1}{2}

= \frac{1}{2} + \frac{2 3}{3}

sin (\frac{π}{3} - arctan (\frac{1}{3}))

5 + 4 cos (\frac{π}{3})

ln (tan (\frac{π}{4}))

\frac{cos ( \frac{π}{6} )}{( 1 - sin ( \frac{π}{6} ) ) ^{2}}

arctan (\frac{5}{15})

What is the value of cos(arctan(-sqrt(3)))+csc(arcsec(2)) ?
The value of cos(arctan(-sqrt(3)))+csc(arcsec(2)) is 1/2+(2sqrt(3))/3