What is the general solution for arcsec(x)=arcsec(2) ?

The general solution for arcsec(x)=arcsec(2) is x=2

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arcsec(x)=arcsec(2)

arcsec (x) = arcsec (2)

x = 2

Solution steps

arcsec (x) = arcsec (2)

arcsec (2) = \frac{π}{3}

arcsec (2)

Use the following trivial identity:

arcsec (2) = \frac{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{π}{3}

= \frac{π}{3}

arcsec (x) = \frac{π}{3}

Apply trig inverse properties

arcsec (x) = \frac{π}{3}

arcsec (x) = a \Rightarrow x = sec (a)

x = sec (\frac{π}{3})

sec (\frac{π}{3}) = 2

sec (\frac{π}{3})

Use the following trivial identity:

sec (\frac{π}{3}) = 2

sec (\frac{π}{3})

sec (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= 2

= 2

x = 2

x = 2

tan^{2} (x) + (3 - 1) tan (x) - 3 = 0

sin (θ) = \frac{2}{7}

2 sec (x) - 5 = 0

tan (a) + cot (a) = sec (a) cos (a)

- 5 tan^{2} (θ) + 3 = 8 tan (θ) + 6

What is the general solution for arcsec(x)=arcsec(2) ?
The general solution for arcsec(x)=arcsec(2) is x=2