What is the value of cos((3pi)/7)cos((2pi}{21})+sin((3pi)/7)sin(\frac{2pi)/(21)) ?

The value of cos((3pi)/7)cos((2pi}{21})+sin((3pi)/7)sin(\frac{2pi)/(21)) is 1/2

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cos((3pi)/7)cos((2pi}{21})+sin((3pi)/7)sin(\frac{2pi)/(21))

cos (\frac{3 π}{7}) cos (\frac{2 π}{21}) + sin (\frac{3 π}{7}) sin (\frac{2 π}{21})

\frac{1}{2}

Solution steps

cos (\frac{3 π}{7}) cos (\frac{2 π}{21}) + sin (\frac{3 π}{7}) sin (\frac{2 π}{21})

Rewrite using trig identities:

cos (\frac{π}{3})

= cos (\frac{π}{3})

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

= \frac{1}{2}

arcsin (- \frac{4}{5})

4 cos (4 5^{\circ})

sin (2) (30)

sin (19 0^{\circ})

cot (\frac{5 π}{2})

What is the value of cos((3pi)/7)cos((2pi}{21})+sin((3pi)/7)sin(\frac{2pi)/(21)) ?
The value of cos((3pi)/7)cos((2pi}{21})+sin((3pi)/7)sin(\frac{2pi)/(21)) is 1/2