How do you find the value of $tan 60$ $tan60$ using the double angle identity?

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How do you find the value of $tan 60$ $tan60$ using the double angle identity?

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Answer 1 · 2017-10-18T14:15:41

$\sqrt{3}$ $sqrt3$

Explanation:

Use trig identity:
$tan 2 a = \frac{2 tan a}{1 - {tan}^{2} a}$ $tan 2a = (2tan a)/(1 - tan^2 a)$
In this case:
$tan (60) = \frac{2 tan (30)}{1 - {tan}^{2} 30}$ $tan (60) = (2tan (30))/( 1 - tan^2 30)$
Trig table gives --> $tan 30 = \frac{\sqrt{3}}{3}$ $tan 30 = sqrt3/3$ --> ${tan}^{2} 30 = \frac{3}{9} = \frac{1}{3}$ $tan^2 30 = 3/9 = 1/3$ -->
$(1 - {tan}^{2} 30) = 1 - \frac{1}{3} = \frac{2}{3}$ $(1 - tan^2 30) = 1 - 1/3 = 2/3$

$tan (60) = (\frac{2 \sqrt{3}}{3}) (\frac{3}{2}) = \sqrt{3}$ $tan (60) = ((2sqrt3)/3)(3/2) = sqrt3$

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How do you find the value of $tan 60$ $tan60$ using the double angle identity?

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How do you find the value of tan60tan60 using the double angle identity?

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How do you find the value of $tan 60$ $tan60$ using the double angle identity?