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

The value of (cos(90))(cos(30))-(sin(90))(sin(30)) is -1/2

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

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

- \frac{1}{2}

Solution steps

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

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

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

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

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

Simplify

= - \frac{1}{2}

+ cos (0)

8 sin (0.03858) e^{- 0.03858} - 1

arccos (\frac{- 19}{29 \cdot 50})

arctan (\frac{- \frac{4}{3}}{- 4})

- 500 cos (4 5^{\circ})

What is the value of (cos(90))(cos(30))-(sin(90))(sin(30)) ?
The value of (cos(90))(cos(30))-(sin(90))(sin(30)) is -1/2