Question

Which of the following is the exact value of cosine of pi times cosine of pi over 3 minus sine of pi times sin of pi over 3

Answer 1

We know that sin(π) = 0, so this expression is equivalent to:

`\cos \pi\cdot\cos (\pi)/(3)-\sin \pi\cdot\sin (\pi)/(3)=\cos \pi\cdot\cos (\pi)/(3)`

Then, using the following known results:

`\begin{gathered} \cos \pi=-1 \\ \cos (\pi)/(3)=(1)/(2) \end{gathered}`

We conclude that:

`\cos \pi\cdot\cos (\pi)/(3)-\sin \pi\cdot\sin (\pi)/(3)=-(1)/(2)`