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If x=30 degree then,verify that ....tan …

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If x=30 degree then,verify that ....tan 2 x = 2 tan x - 1/tan x.

Posted by Aayushi Umariya 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

We have,
{tex} x = 30 ^ { \circ }{/tex}
{tex} \Rightarrow 2 x = 60 ^ { \circ }{/tex}
{tex}L.H.S=\;\tan2x=\tan60^\circ=\sqrt3{/tex}
and, {tex}R.H.S=\frac{2\tan x}{1-\tan^2x}{/tex}
{tex} = \frac { 2 \tan 30 ^ { \circ } } { 1 - \tan ^ { 2 } 30 ^ { \circ } }{/tex}
{tex} = \frac { 2 \times \frac { 1 } { \sqrt { 3 } } } { 1 - \left( \frac { 1 } { \sqrt { 3 } } \right) ^ { 2 } }{/tex}
{tex} = \frac { 2 / \sqrt { 3 } } { 1 - \frac { 1 } { 3 } }{/tex}
{tex} = \frac { 2 / \sqrt { 3 } } { 2 / 3 }{/tex}
{tex} = \frac { 2 } { \sqrt { 3 } } \times \frac { 3 } { 2 } = \sqrt { 3 }{/tex}

therefore, L.H.S = R.H.S

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