What is the value of cos(75)-cos(15) ?

The value of cos(75)-cos(15) is -(sqrt(2))/2

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cos(75)-cos(15)

cos (7 5^{\circ}) - cos (1 5^{\circ})

- \frac{2}{2}

Solution steps

cos (7 5^{\circ}) - cos (1 5^{\circ})

Rewrite using trig identities:

- 2 sin (4 5^{\circ}) sin (3 0^{\circ})

= - 2 sin (4 5^{\circ}) sin (3 0^{\circ})

Use the following trivial identity:

sin (4 5^{\circ}) = \frac{2}{2}

Use the following trivial identity:

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

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

Simplify

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

= - \frac{2}{2}

arctan (- \frac{2}{2})

sin (6 0^{\circ} - 4 5^{\circ})

15 \cdot sin (3 0^{\circ})

4 sin (π)

csc (- 13 5^{\circ})

What is the value of cos(75)-cos(15) ?
The value of cos(75)-cos(15) is -(sqrt(2))/2