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

The value of cos(60-45) is (sqrt(2)(1+sqrt(3)))/4

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cos(60-45)

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

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

Solution steps

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

Rewrite using trig identities:

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

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

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

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

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

Simplify

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

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

sin (2 π)

cos (2 x) = \frac{3}{2}

sin (27 0^{\circ})

- csc^{2} (\frac{π}{4})

cot (9 0^{\circ})

What is the value of cos(60-45) ?
The value of cos(60-45) is (sqrt(2)(1+sqrt(3)))/4