What is the value of (cos(arcsin(1/2)))/(tan(arccos(-1/2))) ?

The value of (cos(arcsin(1/2)))/(tan(arccos(-1/2))) is -1/2

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(cos(arcsin(1/2)))/(tan(arccos(-1/2)))

\frac{cos ( arcsin ( \frac{1}{2} ) )}{tan ( arccos ( - \frac{1}{2} ) )}

- \frac{1}{2}

Decimal Notation

- 0.5

Solution steps

\frac{cos ( arcsin ( \frac{1}{2} ) )}{tan ( arccos ( - \frac{1}{2} ) )}

Rewrite using trig identities:

cos (arcsin (\frac{1}{2})) = \frac{3}{2}

cos (arcsin (\frac{1}{2}))

Rewrite using trig identities:

cos (arcsin (\frac{1}{2})) = 1 - (\frac{1}{2})^{2}

Use the following identity:

cos (arcsin (x)) = 1 - x^{2}

= 1 - (\frac{1}{2})^{2}

= 1 - (\frac{1}{2})^{2}

Simplify

= \frac{3}{2}

Rewrite using trig identities:

tan (arccos (- \frac{1}{2})) = - 3

tan (arccos (- \frac{1}{2}))

Rewrite using trig identities:

tan (arccos (- \frac{1}{2})) = \frac{1 - ( - \frac{1}{2} ) ^{2}}{( - \frac{1}{2} )}

Use the following identity:

tan (arccos (x)) = \frac{1 - x ^{2}}{x}

= \frac{1 - ( - \frac{1}{2} ) ^{2}}{( - \frac{1}{2} )}

= \frac{1 - ( - \frac{1}{2} ) ^{2}}{- \frac{1}{2}}

Simplify

= - 3

= \frac{\frac{3}{2}}{- 3}

Simplify

\frac{\frac{3}{2}}{- 3} : - \frac{1}{2}

\frac{\frac{3}{2}}{- 3}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{\frac{3}{2}}{3}

Apply the fraction rule:

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

\frac{\frac{3}{2}}{3} = \frac{3}{2 3}

= - \frac{3}{2 3}

Cancel the common factor:

3

= - \frac{1}{2}

= - \frac{1}{2}

\frac{π}{3} - sin (\frac{π}{3})

cos (187. 5^{\circ})

1 + cos (12 0^{\circ})

2 - 2 cosh (1)

\frac{cot ^{2} ( 3 5 ^{\circ} )}{cot ^{2} ( 2 5 ^{\circ} )}

What is the value of (cos(arcsin(1/2)))/(tan(arccos(-1/2))) ?
The value of (cos(arcsin(1/2)))/(tan(arccos(-1/2))) is -1/2