Question

Решите пример tg10tg80+ctg20ctg70 с объяснением ​

Answer 1

$tg10^\circ \cdot tg80^\circ +ctg20^\circ \cdot ctg70^\circ =tg10^\circ \cdot tg(90^\circ -10^\circ )+ctg20^\circ \cdot ctg(90^\circ -20^\circ )=\\\\=tg10^\circ \cdot ctg10^\circ +ctg20^\circ \cdot tg20^\circ =1+1=2\\\\\\\star \; \; tg(90^\circ -\alpha )=ctg\alpha \; \; \; ,\; \; \; ctg(90^\circ -\alpha )=tg\alpha \; \; \star \\\\\star \; \; tg\alpha \cdot ctg\alpha =1\; \; \star$