What is the value of cos(60+225) ?

The value of cos(60+225) is (sqrt(2)(sqrt(3)-1))/4

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cos(60+225)

cos (6 0^{\circ} + 22 5^{\circ})

\frac{2 ( 3 - 1 )}{4}

Solution steps

cos (6 0^{\circ} + 22 5^{\circ})

Simplify

= cos (28 5^{\circ})

Rewrite using trig identities:

cos (15 0^{\circ}) cos (13 5^{\circ}) - sin (15 0^{\circ}) sin (13 5^{\circ})

= cos (15 0^{\circ}) cos (13 5^{\circ}) - sin (15 0^{\circ}) sin (13 5^{\circ})

Use the following trivial identity:

cos (15 0^{\circ}) = - \frac{3}{2}

Use the following trivial identity:

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

Use the following trivial identity:

sin (15 0^{\circ}) = \frac{1}{2}

Use the following trivial identity:

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

= (- \frac{3}{2}) (- \frac{2}{2}) - \frac{1}{2} \cdot \frac{2}{2}

Simplify

(- \frac{3}{2}) (- \frac{2}{2}) - \frac{1}{2} \cdot \frac{2}{2} : \frac{2 ( 3 - 1 )}{4}

= \frac{2 ( 3 - 1 )}{4}

2 sin (1 3^{\circ}) cos (1 3^{\circ})

- cos (\frac{π}{4}) - sin (\frac{π}{4})

15 \cdot cos (3 7^{\circ})

cos^{2} (16 0^{\circ})

cos (arctan (- 8))

What is the value of cos(60+225) ?
The value of cos(60+225) is (sqrt(2)(sqrt(3)-1))/4