Question Number 144589 by ZiYangLee last updated on 26/Jun/21
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\underset{{k}=\mathrm{1}} {\overset{\mathrm{90}} {\sum}}\mathrm{sin}\:{k}°+\underset{{k}=\mathrm{1}} {\overset{\mathrm{90}} {\sum}}\mathrm{cos}\:\left(\mathrm{90}°+{k}°\right) \\ $$
Answered by Dwaipayan Shikari last updated on 26/Jun/21
$$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{cos}\left(\frac{\pi}{\mathrm{2}}+\frac{\pi{k}}{\mathrm{180}}\right)=−\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{sin}\left(\frac{\pi{k}}{\mathrm{180}}\right) \\ $$$${So}\:{it}\:{is}\:\mathrm{0} \\ $$