Is arcsin(x)= 1/(sin(x)) ?

The answer to whether arcsin(x)= 1/(sin(x)) is False

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prove arcsin(x)= 1/(sin(x))

prove

arcsin (x) = \frac{1}{sin ( x )}

False

Solution steps

arcsin (x) = \frac{1}{sin ( x )}

Show that the two sides are not equal

For

arcsin (x) = \frac{1}{sin ( x )}

plug in

x = 1

arcsin (1) = \frac{π}{2} (Decimal : Degrees : 1.57079 \dots 9 0^{\circ})

arcsin (1)

Use the following trivial identity:

arcsin (1) = \frac{π}{2}

arcsin (1)

x 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arcsin (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} arcsin (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ}

= \frac{π}{2}

= \frac{π}{2}

\frac{1}{sin ( 1 )} = 1.18839 \dots

\frac{1}{sin ( 1 )}

Refine to a decimal form

= 1.18839 \dots

The two sides are not equal

\Rightarrow False