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

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

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sin(255)-sin(195)

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

- \frac{2}{2}

Solution steps

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

Rewrite using trig identities:

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

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

Use the following trivial identity:

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

Rewrite using trig identities:

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

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

Simplify

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

= - \frac{2}{2}

30 sin (2 0^{\circ})

cos (- \frac{19 π}{12})

sec (arctan (\frac{7}{9}))

arccos (\frac{2 5}{5})

cos (\frac{1}{6})

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