What is the value of cos((13pi)/(36))cos(pi/9)+sin((13pi)/(36))sin(pi/9) ?

The value of cos((13pi)/(36))cos(pi/9)+sin((13pi)/(36))sin(pi/9) is (sqrt(2))/2

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cos((13pi)/(36))cos(pi/9)+sin((13pi)/(36))sin(pi/9)

cos (\frac{13 π}{36}) cos (\frac{π}{9}) + sin (\frac{13 π}{36}) sin (\frac{π}{9})

\frac{2}{2}

Solution steps

cos (\frac{13 π}{36}) cos (\frac{π}{9}) + sin (\frac{13 π}{36}) sin (\frac{π}{9})

Rewrite using trig identities:

cos (\frac{π}{4})

= cos (\frac{π}{4})

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

= \frac{2}{2}

4 tan (\frac{π}{2})

85 sin (2 5^{\circ})

arctan (\frac{15}{25})

sin (4 (0)) e^{0}

\frac{8 3}{sin ( 6 0 ^{\circ} )}

What is the value of cos((13pi)/(36))cos(pi/9)+sin((13pi)/(36))sin(pi/9) ?
The value of cos((13pi)/(36))cos(pi/9)+sin((13pi)/(36))sin(pi/9) is (sqrt(2))/2