proof that

1):- (1/(sec a + tan a) ) - (1/cos a) = (1/cos a) -(1/(sec a- tan a))


2):- (cos a/(1- tan a)) + (sin a/ (1-cot a)) = sin a+ cos a


3:)- ((cos a)^3+(sin a)^3 )/(cos a+ sin a) +((cos a)^3 - (sin a)^3 )/(cos a- sin a) =2

Each if these can be solved by substituting the sine and cosine equivalents for the tangent and secant functions, and then doing some algebraic manipulations. If you're having difficulty show us what you've attempted and where you're getting stuck, then we'll help you along.