Question

tan 75° ==>????????????? ​

Answer 1

Answer:

Step-by-step explanation:

∵ tan 75° = tan(45°+30°)

= tan 45°+ tan 30°/ 1 - tan 45° × tan 30°

= 1 + 1/√3 / 1-1×1/√3

= √3+ 1 / √3 / √3-1/√3

⇒√3 + 1 / √3 - 1

Answer 2

HERE'S YOUR ANSWER

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$\tan(75) \\ \\ = \tan(45 + 30) \\ \\ = \frac{ \tan(45) + \tan(30) }{1 - \tan(45) \tan(30) } \\ \\ = \frac{1 + \frac{1}{ \sqrt{3} } }{1 - 1 \times \frac{1}{ \sqrt{3} } } \\ \\ = \frac{ \frac{ \sqrt{3} + 1}{ \sqrt{3} } }{ \frac{ \sqrt{3 } - 1}{ \sqrt{3} } } \\ \\ = \frac{ \sqrt{3} + 1 }{ \sqrt{3} - 1} \\ \\ = \frac{( { \sqrt{3} + 1})^{2} }{(\sqrt{3} - 1) ( \sqrt{3 } -1)} \\ \\ = \frac{3 + 1 + 2 \sqrt{3} }{ {( \sqrt{3} )}^{2} +{1}^{2} } \\ \\ = \frac{4 + 2 \sqrt{3} }{3 - 1} \\ \\ = \frac{2(2 +\sqrt{3}) }{4} \\ \\ = \frac{2 + \sqrt{3} }{2}$

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