Question

demonstrați egalitatea:

tg15•tg35•tg55•tg75=1

Answer 1

$tg 15 \cdot tg 35 = \frac{sin15}{cos15} \cdot \frac{sin75}{cos75} = \frac{2 sin45\cdot cos 30}{2 cos 45 \cdot cos10} = 1$

$tg 35 \cdot tg 55 = \frac{sin35}{cos35} \cdot \frac{sin55}{cos55} = \frac{2sin45\cdot cos30}{2cos45 \cdot cos10} = 1$

$1 \cdot 1 = 1 \Rightarrow \ \texttt{Egalitate adevarata}$

Answer 2

Răspuns:

Explicație pas cu pas: