Is 1/(sec(θ))=arcsec(θ) ?

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

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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

\frac{( cot ( x ) )}{( csc ( x ) )} = cos (x)

\frac{1 + cot ^{2} ( x )}{cot ^{2} ( x )} = sec^{2} (x)

sec^{2} (x) - tan^{2} (x) = sec (x) cos (x)

cos^{2} (4 x) = \frac{1}{2} + \frac{1}{2} cos (16 x)

- 3 sin (35) - 3 sin (15) = - 6 sin (25) cos (10)