What is the value of cos((13pi)/(15))cos(-pi/5)-sin((13pi)/(15))sin(-pi/5) ?

The value of cos((13pi)/(15))cos(-pi/5)-sin((13pi)/(15))sin(-pi/5) is -1/2

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cos((13pi)/(15))cos(-pi/5)-sin((13pi)/(15))sin(-pi/5)

cos (\frac{13 π}{15}) cos (- \frac{π}{5}) - sin (\frac{13 π}{15}) sin (- \frac{π}{5})

- \frac{1}{2}

Solution steps

cos (\frac{13 π}{15}) cos (- \frac{π}{5}) - sin (\frac{13 π}{15}) sin (- \frac{π}{5})

Rewrite using trig identities:

cos (\frac{2 π}{3})

= cos (\frac{2 π}{3})

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

= - \frac{1}{2}

5 cos (4 5^{\circ})

sin (\frac{3 π}{6})

sin^{2} (\frac{1}{2})

cot (\frac{19 π}{6})

tan (\frac{- 5 π}{12})

What is the value of cos((13pi)/(15))cos(-pi/5)-sin((13pi)/(15))sin(-pi/5) ?
The value of cos((13pi)/(15))cos(-pi/5)-sin((13pi)/(15))sin(-pi/5) is -1/2