1) What kind of triangle is ABC if for his angles we have:
sin[2*(alfa)]=2sin[beta]*cos[gama]
2) If acos[alfa] + bsin[alfa]=acos[beta]+b[sin[beta] , prove that sin(alfa+beta)=2ab/(a^2+b^2)
Prove that the triangle ABC is:
a) acute, if and only if tan(alfa)*tan(beta)>1
b) right, if and only if tan(alfa)*tan(beta)=1
c) obtuse, if and only if tan(alfa)*tan(beta)<1
(|2x-3| + x) / (x^2 - 3x + 2) < 1
|(x^2 - 5x + 4) / ( x^2 - 4)| =< 1
Can somebody help me with this quadratic inequalities, please... If you have time, please also give me an idea of how you solved them... Thank you!