What is the value of sin(120+45) ?

The value of sin(120+45) is (sqrt(2)(sqrt(3)-1))/4

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sin(120+45)

sin (12 0^{\circ} + 4 5^{\circ})

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

Solution steps

sin (12 0^{\circ} + 4 5^{\circ})

Rewrite using trig identities:

sin (12 0^{\circ}) cos (4 5^{\circ}) + cos (12 0^{\circ}) sin (4 5^{\circ})

= sin (12 0^{\circ}) cos (4 5^{\circ}) + cos (12 0^{\circ}) sin (4 5^{\circ})

Use the following trivial identity:

sin (12 0^{\circ}) = \frac{3}{2}

Use the following trivial identity:

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

Use the following trivial identity:

cos (12 0^{\circ}) = - \frac{1}{2}

Use the following trivial identity:

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

= \frac{3}{2} \cdot \frac{2}{2} + (- \frac{1}{2}) \frac{2}{2}

Simplify

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

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

arccos (\frac{3}{2 3})

2 cosh (1)

sec (63 0^{\circ})

\frac{16}{sin ( 1 5 ^{\circ} )}

15 \cdot cos (5 0^{\circ})

What is the value of sin(120+45) ?
The value of sin(120+45) is (sqrt(2)(sqrt(3)-1))/4