What is the value of sin(pi/9)cos((2pi)/9)+cos(pi/9)sin((2pi)/9) ?

The value of sin(pi/9)cos((2pi)/9)+cos(pi/9)sin((2pi)/9) is (sqrt(3))/2

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sin(pi/9)cos((2pi)/9)+cos(pi/9)sin((2pi)/9)

sin (\frac{π}{9}) cos (\frac{2 π}{9}) + cos (\frac{π}{9}) sin (\frac{2 π}{9})

\frac{3}{2}

Solution steps

sin (\frac{π}{9}) cos (\frac{2 π}{9}) + cos (\frac{π}{9}) sin (\frac{2 π}{9})

Rewrite using trig identities:

sin (\frac{π}{3})

= sin (\frac{π}{3})

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

= \frac{3}{2}

cot (6 0^{\circ}) tan (3 0^{\circ}) + sec^{2} (4 5^{\circ})

arctan (\frac{20}{40})

110 cos (15 0^{\circ})

cos^{2} (27 0^{\circ})

2 cos^{2} (\frac{π}{5}) - 1

What is the value of sin(pi/9)cos((2pi)/9)+cos(pi/9)sin((2pi)/9) ?
The value of sin(pi/9)cos((2pi)/9)+cos(pi/9)sin((2pi)/9) is (sqrt(3))/2