Let's simplify the given expression step by step:

cos$7\pi /2+a$ = cos$3\pi /2+2\pi +a$ = cos$3\pi /2+a$ = -sin$a$

tan$\pi /2-a$ = cot$a$ $$usingthetrigonometricidentitytan(x)=1/cot(x)$$

sin$\pi /2-a$ = cos$a$ $$usingthetrigonometricidentitysin(x)=cos(\pi /2-x)$$

cot$3\pi /2-a$ = tan$a$

Now, substituting these simplifications back into the original expression, we get:

-sin$a$ * cot$a$ - cos$a$ + tan$a$

= -sin$a$ * cot$a$ - cos$a$ + sin$a$/cos$a$

= -sin$a$ * cot$a$ - cos$a$ + sin$a$/cos$a$

= -csc$a$ * cot$a$ - cos$a$ + csc$a$

Therefore, the simplified expression is: -csc$a$ * cot$a$ - cos$a$ + csc$a$