Question

tg 7pi/8+ctg 7pi/8 помогите нужно очень срочно

Answer 1

$tg (\pi+\frac{ \pi }{8}) +ctg(\pi+ \frac{ \pi }{8}) =tg \frac{ \pi }{8} +ctg \frac{ \pi }{8} = \frac{sin \frac{ \pi }{8} }{cos\frac{ \pi }{8} } + \frac{cos\frac{ \pi }{8} }{sin\frac{ \pi }{8} }= \\ = \frac{sin ^{2}\frac{ \pi }{8}+cos ^{2}\frac{ \pi }{8} }{sin\frac{ \pi }{8} cos\frac{ \pi }{8} }= \frac{1}{ \frac{sin\frac{ \pi }{4} }{2} } = \frac{2}{ \frac{1}{ \sqrt{2} } }=2 \sqrt{2}$

Answer 2

$tg \frac{7 \pi }{8}+ctg \frac{7 \pi }{8} = \frac{sin \frac{7 \pi }{8} }{cos \frac{7 \pi }{8} } +\frac{cos \frac{7 \pi }{8} }{sin \frac{7 \pi }{8} } = \frac{sin ^{2} \frac{7 \pi }{8}+cos ^{2} \frac{7 \pi }{8} }{cos \frac{7 \pi }{8} sin \frac{7 \pi }{8} } =$

$= \frac{1 }{cos \frac{7 \pi }{8} sin \frac{7 \pi }{8} } = \frac{2 }{2cos \frac{7 \pi }{8} sin \frac{7 \pi }{8} } = \frac{2}{sin \frac{7 \pi }{4} } = \frac{2}{sin(2 \pi - \frac{ \pi }{4} )} = \frac{2}{-sin \frac{ \pi }{4} } =- \frac{2}{ \frac{1}{ \sqrt{2} } } =$

$=-2 \sqrt{2}$