Find the value of $$\cos ^2\theta+\cos^2 (\theta+1^{\circ})+\cos^2(\theta+2^{\circ})+......+\cos^2(\theta+179^{\circ})$$
Can anyone teach me where to start with? I've no idea.
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1Use $\cos (90+\theta)= -\sin \theta $ , you'd find enough pairs. :D – Someone May 22 '15 at 15:30
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I am not claiming that this is the best approach, but you could try and use double angle formula $$cos(2\theta)=2cos^2(\theta)-1$$ so this should simplify your equations into $$\frac{cos(2\theta)+1}{2}+\frac{cos(2(\theta+1^{\circ}))+1}{2}+\ldots$$ Now, use Euler's formula (I don't know what people call this) $$e^{ix}=cos(x)+isin(x)$$ and you should spot something there.
Chee Han
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