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}

csc (\frac{9 π}{4})

cos (\frac{4 π}{6})

arcsin (\frac{5}{4})

8 sin (\frac{π}{2})

tan (\frac{- 5 π}{6})

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