What is the value of sin(60)(csc(60)-sin(60)) ?

The value of sin(60)(csc(60)-sin(60)) is 1/4

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sin(60)(csc(60)-sin(60))

sin (6 0^{\circ}) (csc (6 0^{\circ}) - sin (6 0^{\circ}))

\frac{1}{4}

Solution steps

sin (6 0^{\circ}) (csc (6 0^{\circ}) - sin (6 0^{\circ}))

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

Use the following trivial identity:

csc (6 0^{\circ}) = \frac{2 3}{3}

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

Simplify

\frac{3}{2} (\frac{2 3}{3} - \frac{3}{2}) : \frac{1}{4}

= \frac{1}{4}

cos (105 0^{\circ})

cos (\frac{27 π}{2})

arccos (\frac{4}{5 5})

cos (4 5^{\circ}) - csc (3 0^{\circ})

cos (\frac{3 π}{4}) + i sin (\frac{3 π}{4})

What is the value of sin(60)(csc(60)-sin(60)) ?
The value of sin(60)(csc(60)-sin(60)) is 1/4