What is the value of cos(255)-cos(195) ?

The value of cos(255)-cos(195) is (sqrt(2))/2

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cos(255)-cos(195)

cos (25 5^{\circ}) - cos (19 5^{\circ})

\frac{2}{2}

Solution steps

cos (25 5^{\circ}) - cos (19 5^{\circ})

Rewrite using trig identities:

- 2 sin (22 5^{\circ}) sin (3 0^{\circ})

= - 2 sin (22 5^{\circ}) sin (3 0^{\circ})

Rewrite using trig identities:

sin (22 5^{\circ}) = - \frac{2}{2}

Use the following trivial identity:

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

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

Simplify

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

= \frac{2}{2}

1 - 2 sin^{2} (1 5^{\circ})

cos (\frac{5}{4} π)

cot (4)

arctan (1.3)

cot (\frac{7 π}{2})

What is the value of cos(255)-cos(195) ?
The value of cos(255)-cos(195) is (sqrt(2))/2