prove that: tan (2 x 30°) = 2 tan 30 ° 1 – tan 2 30 ° - Mathematics

Question

prove that:

tan (2 x 30°) = $\frac{2 \tan 30 °}{1 - \tan^{2} 30 °}$

Sum

Solution

RHS,

$\frac{2 \tan^{2} 30 °}{1 - \tan^{2} 30 °} = \frac{2 \frac{1}{\sqrt{3}}}{1 - \frac{1}{3}} = \frac{\frac{2}{\sqrt{3}}}{\frac{2}{3}}$

= $\frac{2}{\sqrt{3}} \div \frac{2}{3}$

= $\frac{2}{\sqrt{3}} \times \frac{3}{2}$

= $\frac{3}{\sqrt{3}} = \frac{\sqrt{3} \times (\sqrt{3})}{\sqrt{3}}$

= $\sqrt{3}$

LHS,
tan (2 x 30°) = tan 60° = $\sqrt{3}$
LHS = RHS

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Trigonometric Ratios of Some Special Angles

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Q 4.3 Q 4.2 Q 5.1

Chapter 23: Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios] - Exercise 23 (A) [Page 291]

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Selina Concise Mathematics [English] Class 9 ICSE

Chapter 23 Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Exercise 23 (A) | Q 4.3 | Page 291

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prove that: tan (2 x 30°) = 2 tan 30 ° 1 – tan 2 30 ° - Mathematics

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