What is the value of sin(90)cos(30)-cos(90)sin(30) ?

The value of sin(90)cos(30)-cos(90)sin(30) is (sqrt(3))/2

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sin(90)cos(30)-cos(90)sin(30)

sin (9 0^{\circ}) cos (3 0^{\circ}) - cos (9 0^{\circ}) sin (3 0^{\circ})

\frac{3}{2}

Solution steps

sin (9 0^{\circ}) cos (3 0^{\circ}) - cos (9 0^{\circ}) sin (3 0^{\circ})

Use the following trivial identity:

sin (9 0^{\circ}) = 1

Use the following trivial identity:

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

Use the following trivial identity:

cos (9 0^{\circ}) = 0

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

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

Simplify

= \frac{3}{2}

cos (120 0^{\circ})

\frac{sin ( 6 0 ^{\circ} )}{1 + cos ( 6 0 ^{\circ} )}

2 (cos (\frac{π}{2}) + i sin (\frac{π}{2}))

4 (cos (15 0^{\circ}) + i sin (15 0^{\circ}))

sin (π \cdot 2)

What is the value of sin(90)cos(30)-cos(90)sin(30) ?
The value of sin(90)cos(30)-cos(90)sin(30) is (sqrt(3))/2