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

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

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sin(45+30)

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

\frac{6 + 2}{4}

Solution steps

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

Rewrite using trig identities:

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

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

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

cos (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}

\frac{tan ( π )}{4}

- 2 sin (π)

sin (\frac{13 π}{2})

sec^{2} (\frac{2 π}{3})

sin (\frac{π}{6}) + cos (\frac{π}{6})

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