Cos Progression

Geometry Level 2

$\cos(1^\circ) + \cos(3^\circ) + \cos(5^\circ) + \cdots + \cos(179^\circ) = \, ?$

The answer is 0.

1 solution

Rishabh Jain
Jan 8, 2016

$\color{#3D99F6}{(\text{Using} \cos\theta=-\cos(180°-\theta))}$ just write cos( 179°) as -cos(1°), cos (177° ) as -cos(3°) and so on, terms will cancel in pairs to give answer 0.

How will they cancel??

Mishal Sheik - 5 years, 5 months ago

$\cos(1)+\cos(179)=\cos(1)-\cos(1)=0$ and they would keep cancelling in pairs upto $\cos(89)$ and $\cos(91)$ .

Department 8 - 5 years, 5 months ago

Thanks....Now I understood....!!

Mishal Sheik - 5 years, 5 months ago

-cos(1°) will cancel cos(1°), -cos(3°) will cancel cos(3°).... ....-cos (89°) will cancel cos (89°). Hope this helps.

Rishabh Jain - 5 years, 5 months ago

Thanks..Now I understood..!!

Mishal Sheik - 5 years, 5 months ago

Cos Progression

The answer is 0.

1 solution

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