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

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

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cos(45+30)

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

\frac{6 - 2}{4}

Solution steps

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

sin (arcsin (\frac{1}{6}) + arctan (- 4))

sin (- \frac{9 π}{4})

sin (8 9^{\circ})

arccos (\frac{5}{9})

arccos (\frac{7}{10})

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