Is arccsc(x)=sin(x) ?

The answer to whether arccsc(x)=sin(x) is False

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

prove arccsc(x)=sin(x)

prove

arccsc (x) = sin (x)

False

Solution steps

arccsc (x) = sin (x)

Show that the two sides are not equal

For

arccsc (x) = sin (x)

plug in

x = 1

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

arccsc (1)

Use the following trivial identity:

arccsc (1) = \frac{π}{2}

arccsc (1)

x 22 \frac{2 3}{3} 1 arccsc (x) \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} arccsc (x) 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ}

= \frac{π}{2}

= \frac{π}{2}

sin (1) = 0.84147 \dots

sin (1)

Refine to a decimal form

= 0.84147 \dots

The two sides are not equal

\Rightarrow False