Question Number 167144 by mathocean1 last updated on 07/Mar/22
$${Calculate}\: \\ $$$$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{{sin}\left(\mathrm{1}\right)}{{cos}\left({k}\right){cos}\left({k}−\mathrm{1}\right)} \\ $$
Answered by mathsmine last updated on 07/Mar/22
$${sin}\left(\mathrm{1}\right)={sin}\left({k}−\left(\boldsymbol{{k}}−\mathrm{1}\right)\right)=\boldsymbol{{sin}}\left(\boldsymbol{{k}}\right)\boldsymbol{{cos}}\left(\boldsymbol{{k}}−\mathrm{1}\right)−{sin}\left({k}−\mathrm{1}\right){cos}\left({k}\right) \\ $$$$=\underset{\mathrm{1}} {\overset{{n}} {\sum}}{tg}\left({k}\right)−\boldsymbol{{tg}}\left(\boldsymbol{{k}}−\mathrm{1}\right)={tg}\left({n}\right) \\ $$