Is arcsec(x)= 1/(sec(x)) ?

The answer to whether arcsec(x)= 1/(sec(x)) is False

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prove arcsec(x)= 1/(sec(x))

prove

arcsec (x) = \frac{1}{sec ( x )}

False

Solution steps

arcsec (x) = \frac{1}{sec ( x )}

Show that the two sides are not equal

For

arcsec (x) = \frac{1}{sec ( x )}

plug in

x = 1

arcsec (1) = 0 (Degrees : 0^{\circ})

arcsec (1)

Use the following trivial identity:

arcsec (1) = 0

arcsec (1)

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}

= 0

= 0

\frac{1}{sec ( 1 )} = 0.54030 \dots

\frac{1}{sec ( 1 )}

Refine to a decimal form

= 0.54030 \dots

The two sides are not equal

\Rightarrow False

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