What is the value of cos((4pi)/9)cos(pi/9)+sin((4pi)/9)sin(pi/9) ?

The value of cos((4pi)/9)cos(pi/9)+sin((4pi)/9)sin(pi/9) is 1/2

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cos((4pi)/9)cos(pi/9)+sin((4pi)/9)sin(pi/9)

cos (\frac{4 π}{9}) cos (\frac{π}{9}) + sin (\frac{4 π}{9}) sin (\frac{π}{9})

\frac{1}{2}

Solution steps

cos (\frac{4 π}{9}) cos (\frac{π}{9}) + sin (\frac{4 π}{9}) sin (\frac{π}{9})

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}

cot (\frac{5}{4} π)

arcsin (0.367)

\frac{tan ( 10 6 ^{\circ} ) + tan ( - 6 1 ^{\circ} )}{1 - tan ( 10 6 ^{\circ} ) tan ( - 6 1 ^{\circ} )}

- csc^{2} (\frac{7 π}{6})

sin^{2} (6 0^{\circ}) + tan^{2} (6 0^{\circ}) - csc^{2} (3 0^{\circ})

What is the value of cos((4pi)/9)cos(pi/9)+sin((4pi)/9)sin(pi/9) ?
The value of cos((4pi)/9)cos(pi/9)+sin((4pi)/9)sin(pi/9) is 1/2