Question

TgП/8/1-tg^2П/8 помогите срочно!!!!!!!!

Answer 1

$tg \frac{ \pi }{8} -tg^2 \frac{ \pi }{8} = \frac{sin \frac{ \pi }{8} }{cos\frac{\pi}{8}}-\frac{sin^2 \frac{ \pi }{8} }{cos^2\frac{\pi}{8}}=\frac{sin \frac{ \pi }{8}\bullet cos\frac{ \pi }{8} -sin^2\frac{\pi}{8}}{cos^2\frac{\pi}{8}}=\\\\=\frac{\frac{1}{2}(sin0+sin \frac{ \pi }{4})-sin^2\frac{\pi}{8} }{cos^2\frac{\pi}{8}}=\frac{\frac{1}{2}sin\frac{\pi}{4}-\frac{1-cos\frac{\pi}{4}}{2}}{\frac{1+cos\frac{\pi}{4}}{2}}=\\\\\\=\frac{sin\frac{\pi}{4}-1+cos\frac{\pi}{4}}{1+cos\frac{\pi}{4}}$

$\frac{ \frac{ \sqrt{2}}{2}-1+\frac{\sqrt{2}}{2}}{1+\frac{\sqrt{2}}{2}}=\frac{\sqrt{2}-1}{\frac{2+\sqrt{2}}{2}}=\frac{2\sqrt{2}-2}{\sqrt{2}+2}.$