Question Number 164758 by mathlove last updated on 21/Jan/22
$${tan}\mathrm{22}=\frac{\mathrm{2}}{\mathrm{5}} \\ $$$$\frac{{sin}\mathrm{112}+{sin}\mathrm{202}}{{cos}\left(−\mathrm{68}\right)}=? \\ $$
Answered by Rasheed.Sindhi last updated on 21/Jan/22
$$\frac{\mathrm{sin}\:\mathrm{112}+\mathrm{sin}\:\mathrm{202}}{\mathrm{cos}\:\left(−\mathrm{68}\right)} \\ $$$$=\frac{\mathrm{sin}\left(\mathrm{90}+\mathrm{22}\right)+\mathrm{sin}\left(\mathrm{180}+\mathrm{22}\right)}{\:\mathrm{cos}\left(\mathrm{22}−\mathrm{90}\right)} \\ $$$$=\frac{\mathrm{cos22}−\mathrm{sin22}\:\:}{\mathrm{sin22}\:} \\ $$$$=\frac{\mathrm{cos22}}{\mathrm{sin22}}−\mathrm{1} \\ $$$$=\frac{\mathrm{1}}{\mathrm{tan22}\:}−\mathrm{1} \\ $$$$=\frac{\mathrm{5}}{\mathrm{2}}−\mathrm{1}=\frac{\mathrm{3}}{\mathrm{2}} \\ $$
Commented by mathlove last updated on 21/Jan/22
$${thanks} \\ $$