Question

The value of $2({\cos }^{2}73°+{\cos }^{2}47°)-\cos 154°$ is

• A. $0$
• B. $-1$
• C. $1$
• D. $2$

Answer 1

The correct option is D $2$

$2({\cos }^{2}73°+{\cos }^{2}47°)-\cos 154°=2({\cos }^{2}73°+1-{\sin }^{2}47°)-\cos (180°-26°)=2(1+\cos (73°+47°\left)\cos \right(73°-47°\left)\right)+\cos 26°=2(1+\cos 120°\cdot \cos 26°)+\cos 26°=2-\cos 26°+\cos 26°(\because \cos 120°=-1/2)=2$