Question

$\cos ({40}^o+\theta )+\cos ({120}^o+\theta )+\cos ({220}^o+\theta )+\cos ({300}^o+\theta )=$

• A. 3
• B. 2
• C. 1
• D. 0

Answer 1

The correct option is D 0

$\cos ({40}^{\circ }+\theta )+\cos ({120}^{\circ }+\theta )+\cos ({220}^{\circ }+\theta )+\cos ({300}^{\circ }+\theta )$

$⟹\cos ({40}^{\circ }+\theta )+\cos ({120}^{\circ }+\theta )+\cos ({180}^{\circ }+({40}^{\circ }+\theta \left)\right)+\cos ({180}^{\circ }+({120}^{\circ }+\theta \left)\right)$

$⟹\cos ({40}^{\circ }+\theta )+\cos ({120}^{\circ }+\theta )-\cos ({40}^{\circ }+\theta )-\cos ({120}^{\circ }+\theta )$ $(\because \cos ({180}^{\circ }+\theta )=-\cos \theta )$

$⟹0$