Answer
$\sin^{2}x\cot^{2}x+\cos^{2}x\tan^{2}x=1$
Work Step by Step
$\sin^{2}x\cot^{2}x+\cos^{2}x\tan^{2}x=1$
Substitute $\cot^{2}x$ by $\dfrac{\cos^{2}x}{\sin^{2}x}$ and $\tan^{2}x$ by $\dfrac{\sin^{2}x}{\cos^{2}x}$:
$\sin^{2}x\Big(\dfrac{\cos^{2}x}{\sin^{2}x}\Big)+\cos^{2}x\Big(\dfrac{\sin^{2}x}{\cos^{2}x}\Big)=1$
Evaluate the products indicated on the left side:
$\cos^{2}x+\sin^{2}x=1$
$\sin^{2}x+\cos^{2}x=1$
Since $\sin^{2}x+\cos^{2}x=1$, the identity is proved:
$1=1$
