Given the real number a calculate tan2a if sina + cosa = 1

sina+cosa = 1

To find tan 2a
.

We  put cosa = sqrt(1-sin^2a) in the given
equation:

sina +sqrt(1-sin^2a) =
1

sqrt(1-sin^2a) =
1-sina.

Square both
sides:

1-sin^2a = 1 -2sina
+sin^2a

0 = -2sina +
2sin^2a

2sina(sina -1) =
0

sina = 0. Or sina = 1.

For
sina = 0 , we get:a = 0. , or a = pi. 

For sina = 1, a = 90
degree.

 Therefore  , when a = 0 or pi,   tan2a =
0

When a = pi/2 or 90 degree,  tan2a = tan pi =
0

So  tan2a = 0.