Math  /  Trigonometry

Question=cos(7π85π24)==\cos \left(\frac{7 \pi}{8}-\frac{5 \pi}{24}\right)=

Studdy Solution
Calculate cos(7π8) \cos \left(\frac{7 \pi}{8}\right) , cos(5π24) \cos \left(\frac{5 \pi}{24}\right) , sin(7π8) \sin \left(\frac{7 \pi}{8}\right) , and sin(5π24) \sin \left(\frac{5 \pi}{24}\right) .
However, since we have already simplified the angle to 2π3 \frac{2 \pi}{3} , we can directly find:
cos(2π3)=12 \cos\left(\frac{2 \pi}{3}\right) = -\frac{1}{2}
The value of the expression is:
12 \boxed{-\frac{1}{2}}

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