Trigonometry 1

sinA=h/a
cosB=h/b
a^3sinA+b^3cosB
=a^3(h/a)+b^3(h/b)
=a^2h+b^2h
=h(a^2+b^2)
=hc^2
=abc (since ab/2=hc/2, the area of triangle ABC)
1/a^2+1/b^2
=(a^2+b^2)/(ab)^2
=c^2/(ab)^2
=(c/ab)^2
=1/h^2 ( ab/2=hc/2, c/ab=1/h)