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

The value of arctan(sqrt(3))-arcsec(-2) is -pi/3

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arctan(sqrt(3))-arcsec(-2)

arctan (3) - arcsec (- 2)

- \frac{π}{3}

Decimal

- 60

Solution steps

arctan (3) - arcsec (- 2)

Use the following trivial identity:

arctan (3) = \frac{π}{3}

arctan (3)

x 0 \frac{3}{3} 13 arctan (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} arctan (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ}

= \frac{π}{3}

Use the following trivial identity:

arcsec (- 2) = \frac{2 π}{3}

arcsec (- 2)

x 1 \frac{2 3}{3} 22 - 2 - 2 - \frac{2 3}{3} - 1 arcsec (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} π arcsec (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} 18 0^{\circ}

= \frac{2 π}{3}

= \frac{π}{3} - \frac{2 π}{3}

Simplify

\frac{π}{3} - \frac{2 π}{3} : - \frac{π}{3}

\frac{π}{3} - \frac{2 π}{3}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{π - 2 π}{3}

Add similar elements:

π - 2 π = - π

= \frac{- π}{3}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{π}{3}

= - \frac{π}{3}

What is the value of arctan(sqrt(3))-arcsec(-2) ?
The value of arctan(sqrt(3))-arcsec(-2) is -pi/3