Question

Fie a,b apartin (-pi/2;pi/2) stiind ca a+b=pi/4. Sa se arate ca tga*tgb+tga+tgb=1

Answer 1

$tg(a+b)=tg\dfrac{\pi}4=1=\dfrac{tga+tgb}{1-tga\cdot tgb},\ deci\;tga+tgb=1-tga\cdot tgb.\\\\Rezult\breve{a}\;c\breve{a}:\;tga\cdot tgb+tga+tgb=1,\ ceea\ ce\ trebuia\;demonstrat.$

Green eyes.