Question

if theta is equals to 30 degree verify that tan 2 theta is equals to 2 tan theta upon 1 minus tan square theta​

Answer 1

Hey friend!

Here is your answer:

Question: if Θ is equals to 30° verify that tan 2Θ is equals to 2 tanΘ / 1 - tan²Θ.

LHS = tan 2Θ

      = tan 60°

      = √3

Now,

RHS = 2 tan Θ/ 1 - tan²Θ

       = 2 tan 30°/ 1 - tan²30°

       = (2 × 1/√3) / 1 - (1/√3)²

       = 2/[√3 × ( 1 - 1/3 )]

       = 2/[√3 × 2/3]

       = 3/√3

       = √3

∵ LHS = RHS,

hence verified

I hope you understand. And if you appreciate my answer, please respond with a thanks.

Answer 2

Answer:

Explanation:

LHS tan 2$\alpha$= tan 2(30°)

                   = tan 60°

                    =$\sqrt{3}$

RHS $tan30\\^{2}$$\frac{2tan\alpha }{1-tan^{2}\alpha }$ =$2 tan 30$°/1-tan 30 x tan30

                            = 2($\frac{1}{\sqrt{3} }$)/1-($\frac{1}{\sqrt{3} }$)($\frac{1}{\sqrt{3} }$)

                              = $\sqrt{3}$

                       HENCE PROVED