Question : The value of $\cos \ 0°+\cos\ 1°+\cos\ 2°......\cos\ 180°$ is:
Option 1: $0$
Option 2: $1$
Option 3: $\frac{\sqrt3}{2}$
Option 4: $\frac{1}{2}$
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Correct Answer: $0$
Solution :
Given: $\cos 0°+\cos 1°+\cos 2°......\cos 180°$
We know the trigonometric identity, $\cos \theta+\cos (180°–\theta)=0$.
$\cos 0°+\cos 1°+\cos 2°......\cos 180°= (\cos 0°+\cos 180°)+(\cos\ 1°+\cos 179°)......(\cos 89°+\cos 91°)+\cos\ 90°= 0$
Hence, the correct answer is $0$.
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