What is the value of cos(300)cos(15)-sin(300)sin(15) ?

The value of cos(300)cos(15)-sin(300)sin(15) is (sqrt(2))/2

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cos(300)cos(15)-sin(300)sin(15)

cos (30 0^{\circ}) cos (1 5^{\circ}) - sin (30 0^{\circ}) sin (1 5^{\circ})

\frac{2}{2}

Solution steps

cos (30 0^{\circ}) cos (1 5^{\circ}) - sin (30 0^{\circ}) sin (1 5^{\circ})

Rewrite using trig identities:

cos (31 5^{\circ})

= cos (31 5^{\circ})

Rewrite using trig identities:

cos (18 0^{\circ}) cos (13 5^{\circ}) - sin (18 0^{\circ}) sin (13 5^{\circ})

= cos (18 0^{\circ}) cos (13 5^{\circ}) - sin (18 0^{\circ}) sin (13 5^{\circ})

Use the following trivial identity:

cos (18 0^{\circ}) = (- 1)

Use the following trivial identity:

cos (13 5^{\circ}) = - \frac{2}{2}

Use the following trivial identity:

sin (18 0^{\circ}) = 0

Use the following trivial identity:

sin (13 5^{\circ}) = \frac{2}{2}

= (- 1) (- \frac{2}{2}) - 0 \cdot \frac{2}{2}

Simplify

= \frac{2}{2}

2 cos (2 π)

\frac{0.5}{sin ( 0.5 )}

18 sin (7 3^{\circ})

(- 3 + i) (\frac{1}{8} (cos (\frac{5 π}{3}) + i sin (\frac{5 π}{3})))

arccos (\frac{2}{4})

What is the value of cos(300)cos(15)-sin(300)sin(15) ?
The value of cos(300)cos(15)-sin(300)sin(15) is (sqrt(2))/2