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

The value of sin(15)cos(15)+cos(15)sin(15) is (sin(pi/6)+2cos(pi/(12))sin(pi/(12)))/2

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

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

\frac{sin ( \frac{π}{6} ) + 2 cos ( \frac{π}{12} ) sin ( \frac{π}{12} )}{2}

Decimal Notation

0.5

Solution steps

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

Rewrite using trig identities:

sin (1 5^{\circ}) cos (1 5^{\circ}) = \frac{sin ( 3 0 ^{\circ} )}{2}

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

Use the Double Angle identity:

2 sin (x) cos (x) = sin (2 x)

sin (x) cos (x) = \frac{sin ( 2 x )}{2}

= \frac{sin ( 2 \cdot 1 5 ^{\circ} )}{2}

Simplify

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

= \frac{sin ( 3 0 ^{\circ} )}{2} + cos (1 5^{\circ}) sin (1 5^{\circ})

Simplify

= \frac{sin ( 3 0 ^{\circ} ) + 2 cos ( 1 5 ^{\circ} ) sin ( 1 5 ^{\circ} )}{2}

sin (\frac{π}{2}) - sin (\frac{π}{4})

arccos (\frac{7}{11})

sec (- 21 0^{\circ})

arctan (- \frac{8}{6})

cot (9)

What is the value of sin(15)cos(15)+cos(15)sin(15) ?
The value of sin(15)cos(15)+cos(15)sin(15) is (sin(pi/6)+2cos(pi/(12))sin(pi/(12)))/2