Question

cos 35° + cos 85° + cos 155° =
(a) 0

(b) $\frac{1}{\sqrt{3}}$

(c) $\frac{1}{\sqrt{2}}$

(d) cos 275°

Answer 1

(a) 0

$$\begin{gathered} \cos 35°+\cos 85°+\cos 155° \\ =2\cos \left(\frac{35°+85°}{2}\right)\cos \left(\frac{35°-85°}{2}\right)+\cos 155°\left[\because \cos A+\cos B=2\cos \left(\frac{A+B}{2}\right)\cos \left({\displaystyle \frac{A-B}{2}}\right)\right] \\ =2\cos 60°\cos \left(-25°\right)+\cos 155° \\ =2\times \frac{1}{2}\cos 25°+\cos 155° \\ =\cos 25°+\cos 155° \\ =2\cos \left(\frac{25°+155°}{2}\right)\cos \left(\frac{25°-155°}{2}\right) \\ =2\cos 90°\cos 65° \\ =0 \end{gathered}$$