Question

Taking A = 30°, verify the following:
tan 2A =2tanA/1-tan²A​

Answer 1

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Step-by-step explanation:

A = 30°

Now,

L.H.S. = tan2A

          = tan (2*30°)

          = tan 60°

          = √3

Again,

R.H.S.=

$\frac{2tanA}{1-tan^{2}A }\\=\frac{2tan30}{1-tan^{2}30 }\\=\frac{2*\frac{1}{\sqrt{3}}}{1-(\frac{1}{\sqrt{3}})^{2}}\\=\frac{\frac{2}{\sqrt{3}}}{1-\frac{1}{3}}\\=\frac{\frac{2}{\sqrt{3}}}{\frac{3-1}{3}}\\=\frac{2*3}{2*\sqrt{3}}\\=\frac{3}{\sqrt{3}}\\=\sqrt{3}$

Therefore,

L.H.S. = R.H.S. = √3

So,

tan2A = 2tanA/(1 - tan²A) (Verified)

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