Question

The value of ${\cos }^2{10}^{\circ }-\cos {10}^{\circ }\cos {50}^{\circ }+{\cos }^2{50}^{\circ }=$

• A.
• B.
• C.
• D. 3

Answer 1

The correct option is C

${\cos }^2{10}^{\circ }-\cos {10}^{\circ }\cos {50}^{\circ }+{\cos }^2{50}^{\circ }=$
$=\frac{1}{2}\left[1+\cos {20}^{\circ }-\left(\cos {60}^{\circ }+\cos {40}^{\circ }\right)+\left(1+\cos {100}^{\circ }\right)\right]$ $=\frac{1}{2}\left[1+\cos {20}^{\circ }-\frac{1}{2}-\cos {40}^{\circ }+1-\cos {80}^{\circ }\right]=\frac{1}{2}\left[\frac{3}{2}+\cos {20}^{\circ }-\left(2\cos {60}^{\circ }\cos {20}^{\circ }\right)\right]=\frac{3}{4}$