Question

Find the value of $\cos {80}^{\circ }+\cos {40}^{\circ }-\cos {20}^{\circ }$.

Answer 1

Given, $y=\cos {80}^0+\cos {40}^0-\cos {20}^0$

We have trigonometry identity

$\cos a^0+\cos b^0$ $=2\cos \left(\frac{a^0+b^0}{2}\right)\cos \left(\frac{a^0-b^0}{2}\right)$

$y==2\cos \left(\frac{{80}^0+{40}^0}{2}\right)\cos \left(\frac{{80}^0-{40}^0}{2}\right)-\cos {20}^0$

$=2\cos {60}^0\cos {20}^0-\cos {20}^0$

$=2\times \frac{1}{2}\cos {20}^0-\cos {20}^0=0$