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

### 2 Answers | Add Yours

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**

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 .