Trigonometric identity: 

Applying the identities [ tan θ = sin θ / cos θ ] and [ cot θ = cos θ / sin θ ] to the LHS,
Simplifying each rational expression,
Writing sin A  cos A =  (cos A  sin A),
The denominator of both the fractions above is same, cos A  sin A. Adding the two fractions,
Applying the formula a^{2}  b^{2} = (a + b)(a  b),
Canceling the common factor (cos A  sin A) from the numerator and denominator,
= cos A + sin A... which is the RHS expression
Trigonometric identities applied:
 tan θ = sin θ / cos θ
 cot θ = cos θ / sin θ