Question

Using the formula, tan2A = (2tanA) / (1-tan 2 A), find the value of tan 60*; given that tan30* = 1/√3...

Answer 1

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Answer 2

Answer:

The value of $\tan 60 ^ { \circ } = \sqrt { 3 }$

To find:

The value of $\tan 60 ^ { \circ }$

Solution:

We know that  

$\tan ( A + B ) = \frac { \tan A + \tan B } { ( 1 - \tan A \cdot \tan B ) }$

When A=B

$\tan ( A + A ) = \frac { \tan A + \tan A } { 1 - \tan ^ { 2 } A }$

By using A = $30^{\circ}$

$\begin{array} { c } { \tan 60 ^ { \circ } = \frac { \tan 30 ^ { \circ } + \tan 30 ^ { \circ } } { 1 - \tan ^ { 2 } 30 ^ { \circ } } } \\\\ { \tan 60 ^ { \circ } = \frac { \frac { 1 } { \sqrt { 3 } + } \left( \frac { 1 } { \sqrt { 3 } } \right) } { \left( 1 - \left( \frac { 1 } { \sqrt { 3 } } \right) ^ { 2 } \right) } = \frac { \left( \frac { 2 } { \sqrt { 3 } } \right) } { \frac { 2 } { 3 } } = \frac { 2 } { \sqrt { 3 } } \times \frac { 3 } { 2 } = \sqrt { 3 } } \end{array}$