`(tan(x) + cot(y))/(tan(x)cot(y)) = tan(y) + cot(x)` Verfiy the identity.

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Verify the identity: `[tan(x)+cot(y)]/[tan(x)cot(y)]=tan(y)+cot(x)`

Rewrite the left side of the equation as two fractions.

`tan(x)/[tan(x)cot(y)]+cot(y)/[tan(x)cot(y)]=tan(y)+cot(x)`

`1/cot(y)+1/tan(x)=tan(y)+cot(x)`

Simplify the left side of the equation using the following reciprocal identities:

1/cot(y)=tan(y)  and 1/tan(x)=cot(x)

`tan(y)+cot(x)=tan(y)+cot(x)`