What is the value of sin(15)cos(105)+cos(15)sin(105) ?

The value of sin(15)cos(105)+cos(15)sin(105) is (sqrt(3))/2

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sin(15)cos(105)+cos(15)sin(105)

sin (1 5^{\circ}) cos (10 5^{\circ}) + cos (1 5^{\circ}) sin (10 5^{\circ})

\frac{3}{2}

Solution steps

sin (1 5^{\circ}) cos (10 5^{\circ}) + cos (1 5^{\circ}) sin (10 5^{\circ})

Rewrite using trig identities:

sin (12 0^{\circ})

= sin (12 0^{\circ})

Use the following trivial identity:

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

= \frac{3}{2}

arctan (\frac{4}{12})

sin (13 2^{\circ})

4 sin (2)

sin (18 0^{\circ} - 4 5^{\circ})

- arctan (\frac{3}{4})

What is the value of sin(15)cos(105)+cos(15)sin(105) ?
The value of sin(15)cos(105)+cos(15)sin(105) is (sqrt(3))/2