Is 1/(sec(θ))=arcsec(θ) ?

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

prove 1/(sec(θ))=arcsec(θ)

prove

\frac{1}{sec ( θ )} = arcsec (θ)

False

Solution steps

\frac{1}{sec ( θ )} = arcsec (θ)

Show that the two sides are not equal

For

\frac{1}{sec ( θ )} = arcsec (θ)

plug in

θ = 1

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

\frac{1}{sec ( 1 )}

Refine to a decimal form

= 0.54030 \dots

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

The two sides are not equal

\Rightarrow False

p ro v e \frac{( cot ( x ) )}{( csc ( x ) )} = cos (x)

p ro v e \frac{( sec ^{2} ( t ) )}{sec ^{2} ( t ) - 1} = csc^{2} (t)

p ro v e sin^{2} (x) = cos (2 x) + 2

p ro v e 1 + cos^{2} (x) = 2 - sin^{2} (x)

p ro v e sin^{2} (x) = cos (2 x) - 2