Using the formula- tan 2A - 2-tan-A-1-tan2-A- find the value of tan 60- it being given that tan 30-1-3-

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Standard Values of Trigonometric Ratios

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Question

Using the formula, $t a n 2 A = \frac{2 t a n A}{1 - t a n^{2} A^{'}}$ find the value of $t a n 60^{\circ},$ it being given that $t a n 30^{\circ} = \frac{1}{\sqrt{3}} .$

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Solution

Taking the value of $A = 30^{o}$
Now put the value of A in the formula of (tan2A),

$tan space 60 space equals fraction numerator 2 space tan space 30 space over denominator 1 minus tan squared 30 end fraction equals fraction numerator 2 open parentheses begin display style fraction numerator 1 over denominator square root of 3 end fraction end style close parentheses over denominator 1 minus open parentheses begin display style fraction numerator 1 over denominator square root of 3 end fraction end style close parentheses squared end fraction equals fraction numerator begin display style fraction numerator 2 over denominator square root of 3 end fraction end style over denominator 1 minus begin display style 1 third end style end fraction equals fraction numerator begin display style fraction numerator 2 over denominator square root of 3 end fraction end style over denominator begin display style 2 over 3 end style end fraction equals fraction numerator square root of 3 over denominator 2 end fraction$

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Similar questions

Q. Using the formula,

tan 2 A = \frac{2 tan A}{1 - {tan}^{2} A}

, find the value of

tan 60^{\circ}

, it being that

tan 30^{\circ} = \frac{1}{\sqrt{3}}

Q. Using the formula, tan

2 A = \frac{2 \tan A}{1 - \tan^{2} A}

, find the value of tan 60°, it being given that tan 30° =

\frac{1}{\sqrt{3}}

If A = $30^{\circ},$ verify that:

(i) $s i n 2 A = \frac{2 t a n A}{1 + t a n^{2} A}$ (ii) $c o s 2 A = \frac{1 - t a n^{2} A}{1 + t a n^{2} A}$ (iii) $t a n 2 A = \frac{2 t a n A}{1 - t a n^{2} A}$

How many of below given statements are correct?

1. sin2A = 2sinA.cosA

2.cos2A = $s i n^{2} A - c o s^{2} A$

3.tan A = $\frac{2 t a n \frac{A}{2}}{1 - t a n^{2} \frac{A}{2}}$

4. $s i n^{2} \frac{A}{2}$ = 1 - cosA

5. $t a n^{2} A$ = $\frac{1 - c o s 2 A}{1 + c o s 2 A}$

6. $s i n^{2} A$ = $\frac{2 t a n A}{1 - t a n^{2} A}$

Q. If A =

60^{\circ}

verify the following .

t a n 2 A = \frac{2 t a n A}{1 - {t a n}^{2} A}

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Using the formula, tan2A=2 tan A1−tan2 A′ find the value of tan60∘, it being given that tan30∘=1√3.

Taking the value of A=30o Now put the value of A in the formula of (tan2A),

Using the formula, $t a n 2 A = \frac{2 t a n A}{1 - t a n^{2} A^{'}}$ find the value of $t a n 60^{\circ},$ it being given that $t a n 30^{\circ} = \frac{1}{\sqrt{3}} .$