what is (1+tan a )(cot a -1) simplified with steps

Question

equivalent trig expressions

Answer 1

First, remember that tan a = (sin a)/(cos a)   and  cot a = (cos a)/(sin a)

 

Rewrite the expression using those identities, then FOIL and reduce:

 

 

(1+(sin a)/(cos a)) x ((cos a)/(sin a) -1)

 

(cos a)/(sin a) - 1 + 1 - (sin a)/(cos a)

 

(cos a)/(sin a) - (sin a)/(cos a)

 

cot a  -  tan a