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

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Given sin^2 a = 1/2

We need to use different methods to find tan(a)

We will use 2 methods:

First method:

We know that
sin^2 a + cos^2 a = 1

==> cos^2 a = 1- sin^2 a = 1- 1/2 = 1/2

==> cos^2 a = 1/2

==> cos a = +-1/sqrt2

==> sin a = +-1/sqrt2

Now we know that tan(a) = sin(a)/cos(a) = (1/sqrt2)/(1/sqrt2) = 1

==> tan(a) = +-1

 

Second method.

Given that sin^2 a = 1/2

==> sin(a) = +-1/sqrt2

==> a = pi/4

==> tan(a) = tan(pi/4) = +-1

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