What is tan2a if cosa = 1 - sina?

We'll re-write the given constraint cosa = 1 - sina. We'll
add sin a both sides and we'll have:

sin a + cos a =
1

We'll square raise the new relation sina + cosa =
1.

(sina + cosa)^2 =
1^2

(sina)^2 + (cosa)^2 + 2sina*cosa = 1
(1)

But, from the fundamental formula of
trigonometry:

(sina)^2 + (cosa)^2 =
1

We'll substitute (sina)^2 + (cosa)^2 by
1:

The relation (1) will
become:

1 + 2sina*cosa =
1

We'll eliminate like
terms:

 2sina*cosa =
0

But  2sina*cosa = sin
(2a)

We'll write the formula for tan
2a:

tan 2a = sin 2a/cos 2a

tan
2a = 0/cos 2a

tan 2a =
0