Question

Evaluate: $\frac{{\sin }^{3}x+{\cos }^{3}x}{{\sin }^{2}x{\cos }^{2}x}$

Answer 1

$\frac{{\sin }^{3}x+{\cos }^{3}x}{{\sin }^{2}x{\cos }^{2}x}$

$=\frac{{\sin }^{3}x}{{\sin }^{2}x{\cos }^{2}x}+\frac{{\cos }^{3}x}{{\sin }^{2}x{\cos }^{2}x}$

$=\frac{\sin x}{{\cos }^{2}x}+\frac{\cos x}{{\sin }^{2}x}$

$=\frac{\sin x}{\cos x}.\frac{1}{\cos x}+\frac{\cos x}{\sin x}.\frac{1}{\sin x}$

$=\tan x\sec x+\cot x\cos ecx$