What is the value of cos(45-60) ?

The value of cos(45-60) is (sqrt(2)+sqrt(6))/4

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cos(45-60)

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

\frac{2 + 6}{4}

Solution steps

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

Rewrite using trig identities:

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

= cos (4 5^{\circ}) cos (6 0^{\circ}) + sin (4 5^{\circ}) sin (6 0^{\circ})

Use the following trivial identity:

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

Use the following trivial identity:

cos (6 0^{\circ}) = \frac{1}{2}

Use the following trivial identity:

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

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

= \frac{2}{2} \cdot \frac{1}{2} + \frac{2}{2} \cdot \frac{3}{2}

Simplify

\frac{2}{2} \cdot \frac{1}{2} + \frac{2}{2} \cdot \frac{3}{2} : \frac{2 + 6}{4}

= \frac{2 + 6}{4}

tan (6)

arcsin (5)

3 cos (π)

arctan (9)

- cos (π) - (- cos (0))

What is the value of cos(45-60) ?
The value of cos(45-60) is (sqrt(2)+sqrt(6))/4