What is the value of sin((4pi)/7)cos((5pi}{21})-cos((4pi)/7)sin(\frac{5pi)/(21)) ?

The value of sin((4pi)/7)cos((5pi}{21})-cos((4pi)/7)sin(\frac{5pi)/(21)) is (sqrt(3))/2

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sin((4pi)/7)cos((5pi}{21})-cos((4pi)/7)sin(\frac{5pi)/(21))

sin (\frac{4 π}{7}) cos (\frac{5 π}{21}) - cos (\frac{4 π}{7}) sin (\frac{5 π}{21})

\frac{3}{2}

Solution steps

sin (\frac{4 π}{7}) cos (\frac{5 π}{21}) - cos (\frac{4 π}{7}) sin (\frac{5 π}{21})

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}

\frac{sin ( 3 )}{3}

tan (1.5)

cos^{5} (0)

sin (\frac{7 π}{6}) - sin (\frac{π}{3})

cos (4 5^{\circ} - 15 0^{\circ})

What is the value of sin((4pi)/7)cos((5pi}{21})-cos((4pi)/7)sin(\frac{5pi)/(21)) ?
The value of sin((4pi)/7)cos((5pi}{21})-cos((4pi)/7)sin(\frac{5pi)/(21)) is (sqrt(3))/2