The expression tanA1−cotA+cotA1−tanAtanA1-cotA+cotA1-tanA can be written as :

The given expression is:

tanA/(1−cotA) + cotA/(1−tanA)

First, we know that tanA = 1/cotA and cotA = 1/tanA. So, we can rewrite the expression as:

1/cotA/(1−1/tanA) + 1/tanA/(1−1/cotA)

This simplifies to:

1/cotA/(tanA−1) + 1/tanA/(cotA−1)

Now, we can multiply the numerator and denominator of each fraction by tanA*cotA to get rid of the fractions in the denominators:

tanA/(cotAtanA−cotA) + cotA/(tanAcotA−tanA)

This simplifies to:

tanA/(1−cotA) + cotA/(1−tanA)

So, the given expression can be written as:

tanA/(1−cotA) + cotA/(1−tanA)