What is the value of cos(30+45) ?

The value of cos(30+45) is (sqrt(6)-sqrt(2))/4

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cos(30+45)

cos (3 0^{\circ} + 4 5^{\circ})

\frac{6 - 2}{4}

Solution steps

cos (3 0^{\circ} + 4 5^{\circ})

Rewrite using trig identities:

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

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

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

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

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

Simplify

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

= \frac{6 - 2}{4}

9 sin (6 0^{\circ})

3 sin (- \frac{π}{2})

1 cos (4 5^{\circ})

cos^{2} (\frac{π}{12})

arcsin (\frac{5}{10})

What is the value of cos(30+45) ?
The value of cos(30+45) is (sqrt(6)-sqrt(2))/4