What is tan ( a ) if sin^2 ( a ) = 1/2 use different methods.

sin^2a = 1/2.

Therefore sina
= +sqrt(1/2), or - sqrt(1/2).

Therefore  if sina =
sqrt(1/2) a = pi/4, or 3pi/4. So tan a = tanpi/4 or tan (3pi/4) . So tana = 1 or
-1.

If sina = -sqrt(1/2), then a = -5pi/4 or 7pi/4.
Therefore tan(5pi/4) = 1, or tan (7pi/4) = -1.

Therefore
tana = 1 or -1 .