What is the value of sin((3pi)/5)cos(pi/(15))+cos((3pi)/5)sin(pi/(15)) ?

The value of sin((3pi)/5)cos(pi/(15))+cos((3pi)/5)sin(pi/(15)) is (sqrt(3))/2

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sin((3pi)/5)cos(pi/(15))+cos((3pi)/5)sin(pi/(15))

sin (\frac{3 π}{5}) cos (\frac{π}{15}) + cos (\frac{3 π}{5}) sin (\frac{π}{15})

\frac{3}{2}

Solution steps

sin (\frac{3 π}{5}) cos (\frac{π}{15}) + cos (\frac{3 π}{5}) sin (\frac{π}{15})

Rewrite using trig identities:

sin (\frac{2 π}{3})

= sin (\frac{2 π}{3})

Use the following trivial identity:

sin (\frac{2 π}{3}) = \frac{3}{2}

= \frac{3}{2}

arctan (\frac{6}{- 5})

4 sec (\frac{3 π}{4})

cos (\frac{π}{8}) + sin (\frac{π}{8})

2 (cos (30 0^{\circ}) + i sin (30 0^{\circ}))

28 \cdot cos (3 0^{\circ})

What is the value of sin((3pi)/5)cos(pi/(15))+cos((3pi)/5)sin(pi/(15)) ?
The value of sin((3pi)/5)cos(pi/(15))+cos((3pi)/5)sin(pi/(15)) is (sqrt(3))/2