Originally Posted by
andtom $\displaystyle \frac{sin^{4} \alpha}{a}+ \frac{cos ^{4}\alpha }{b}= \frac{1}{a+b}$
take $\displaystyle sin^{2} \alpha=x$. then $\displaystyle cos^{2} \alpha=1-x$.
Now substitute in the given equation. SOLVE the quadratic. the roots are nice! you will get $\displaystyle sin^{2} \alpha=\frac{a}{a+b}$ . Substitute this below
Prove that:
$\displaystyle \frac{sin^{8} \alpha}{a^{3}}+ \frac{cos ^{8} \alpha }{b^{3}}= \frac{1}{(a+b)^{3}}$
Thanks in advance