What is tan 2a when sin a +cos a = 1 ?

First, we'll raise to square the given
constraint:

sin a + cos a =
1

(sin a + cos a)^2 = 1

We'll
expand the square:

(sin a)^2 + 2sin a*cos a + (cos a)^2 =
1

But, from Pythagorean identity, we'll
get:

(sin a)^2 + (cos a)^2 =
1

1 + 2sin a*cos a  = 1

We'll
eliminate 1 both sides:

2sin a*cos a  =
0

We recognize the double angle
identity:

2sin a*cos a  = sin
(2a)

sin (2a)= 0

We'll write
the tangent that has to be determined:

tan (2a) = sin (2a)
/cos (2a)

tan (2a) = 0/cos
(2a)

tan (2a) =
0

The requested tangent is: tan (2a) =
0.