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

The value of sin(105)cos(15) is (sqrt(3)+2)/4

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sin(105)cos(15)

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

\frac{3 + 2}{4}

Solution steps

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

Rewrite using trig identities:

\frac{sin ( 12 0 ^{\circ} ) + sin ( 9 0 ^{\circ} )}{2}

= \frac{sin ( 12 0 ^{\circ} ) + sin ( 9 0 ^{\circ} )}{2}

Use the following trivial identity:

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

Use the following trivial identity:

sin (9 0^{\circ}) = 1

= \frac{\frac{3}{2} + 1}{2}

Simplify

\frac{\frac{3}{2} + 1}{2} : \frac{3 + 2}{4}

= \frac{3 + 2}{4}

sin (6 0^{\circ}) \cdot 10

tan (- \frac{π}{9})

arctan (- 3.16)

sin (2 (\frac{π}{12}))

\frac{- sin ^{2} ( 3 3 ^{\circ} ) - cos ^{2} ( 3 3 ^{\circ} )}{5}

What is the value of sin(105)cos(15) ?
The value of sin(105)cos(15) is (sqrt(3)+2)/4