What is the value of sin(arcsin(1/2)-arccos(0)) ?

The value of sin(arcsin(1/2)-arccos(0)) is -(sqrt(3))/2

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sin(arcsin(1/2)-arccos(0))

sin (arcsin (\frac{1}{2}) - arccos (0))

- \frac{3}{2}

Solution steps

sin (arcsin (\frac{1}{2}) - arccos (0))

Rewrite using trig identities:

sin (arcsin (\frac{1}{2})) cos (arccos (0)) - cos (arcsin (\frac{1}{2})) sin (arccos (0))

= sin (arcsin (\frac{1}{2})) cos (arccos (0)) - cos (arcsin (\frac{1}{2})) sin (arccos (0))

Rewrite using trig identities:

sin (arcsin (\frac{1}{2})) = \frac{1}{2}

Rewrite using trig identities:

cos (arccos (0)) = 0

Rewrite using trig identities:

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

Rewrite using trig identities:

sin (arccos (0)) = 1

= \frac{1}{2} \cdot 0 - \frac{3}{2} \cdot 1

Simplify

= - \frac{3}{2}

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What is the value of sin(arcsin(1/2)-arccos(0)) ?
The value of sin(arcsin(1/2)-arccos(0)) is -(sqrt(3))/2