Question

If =30°, then tan2= 21−2​

Answer 1

Step-by-step explanation:

The given equation is :

tan{\theta}=\frac{2tan{\theta}}{1-tan^{2}{\theta}}tanθ=

1−tan

2

θ

2tanθ

Now, if {\theta}=30^{{\circ}}θ=30

∘

, then the equation becomes,

tan2(30)^{{\circ}}=\frac{2tan30^{{\circ}}}{1-tan^{2}30^{{\circ}}}tan2(30)

∘

=

1−tan

2

30

∘

2tan30

∘

tan60^{{\circ}}=\frac{2{\times}\frac{1}{\sqrt{3}}}{1-\frac{1}{3}}tan60

∘

=

1−

3

1

2×

3

1

\sqrt{3}=\frac{\frac{2}{\sqrt{3}}}{\frac{2}{3}}

3

=

3

2

3

2

\sqrt{3}=\sqrt{3}

3

=

3

Hence proved.