What is the value of ((5arcsin(1))-(5arcsin(-1)))/(1-(-1)) ?

The value of ((5arcsin(1))-(5arcsin(-1)))/(1-(-1)) is (5pi)/2

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((5arcsin(1))-(5arcsin(-1)))/(1-(-1))

\frac{( 5 arcsin ( 1 ) ) - ( 5 arcsin ( - 1 ) )}{1 - ( - 1 )}

\frac{5 π}{2}

Decimal Notation

450

Solution steps

\frac{( 5 arcsin ( 1 ) ) - ( 5 arcsin ( - 1 ) )}{1 - ( - 1 )}

= \frac{5 arcsin ( 1 ) - 5 arcsin ( - 1 )}{1 - ( - 1 )}

Simplify

= \frac{5 arcsin ( 1 ) - 5 arcsin ( - 1 )}{2}

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- 1) = - arcsin (1)

= \frac{5 arcsin ( 1 ) - 5 ( - arcsin ( 1 ) )}{2}

Simplify

= 5 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}

= 5 \cdot \frac{π}{2}

Simplify

5 \cdot \frac{π}{2} : \frac{5 π}{2}

5 \cdot \frac{π}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{π 5}{2}

= \frac{5 π}{2}

2 sin (\frac{3 π}{3})

2 tan (3 6^{\circ})

tan (\frac{π}{2} + \frac{π}{3})

10 cos (\frac{5 π}{3})

- 4 (256 cos (1 6^{\circ}) + 12 sin (1 6^{\circ}))

What is the value of ((5arcsin(1))-(5arcsin(-1)))/(1-(-1)) ?
The value of ((5arcsin(1))-(5arcsin(-1)))/(1-(-1)) is (5pi)/2