From Förberedande kurs i matematik 1

Using the addition formula for cosine, we can express \displaystyle \cos \left( v-{\pi }/{3}\; \right) in terms of \displaystyle \text{cos }v and \displaystyle \text{sin }v,

\displaystyle \cos \left( v-\frac{\pi }{3} \right)=\cos v\centerdot \cos \frac{\pi }{3}+\sin v\centerdot \sin \frac{\pi }{3}

Since \displaystyle \text{cos }v=b\text{ } and \displaystyle \sin v=\sqrt{1-b^{2}} we obtain

\displaystyle \cos \left( v-\frac{\pi }{3} \right)=b\centerdot \frac{1}{2}+\sqrt{1-b^{2}}\centerdot \frac{\sqrt{3}}{2}