39coming to properties of triangles its all about formulaes and interchanging them whenever and wherever the situiation arises.
nothing more of a kinda intelligent stuff over there.
coming to the basics part , u have to remember
sub multiple angle , multiple angle formulae and
half angle formulae and addition, subtraction formulae.
and try to always inter connect the formulas the trigonometry, this i find as the biggest challenge for any student ( once including me).
now for inverse trigonometric funstions , nothing but pure practice would only help u. solve as many questions as u can.