How do you simplify tan4θ to trigonometric function of a unit θ ? Sub Grade: 10

# How do you simplify tan4θ to trigonometric function of a unit θ ? Sub Grade: 10

1. A
$\frac{4\mathit{tan\theta }-4\mathit{ta}{n}^{3}\theta }{1-6\mathit{ta}{n}^{2}\theta +\mathit{ta}{n}^{4}\theta }$
2. B
$\frac{3\mathit{tan\theta }-4\mathit{ta}{n}^{3}\theta }{1-6\mathit{ta}{n}^{2}\theta +\mathit{ta}{n}^{4}\theta }$
3. C
$\frac{6\mathit{tan\theta }-4\mathit{ta}{n}^{3}\theta }{1-6\mathit{ta}{n}^{2}\theta +\mathit{ta}{n}^{4}\theta }$
4. D
$\frac{5\mathit{tan\theta }-4\mathit{ta}{n}^{3}\theta }{1-6\mathit{ta}{n}^{2}\theta +\mathit{ta}{n}^{4}\theta }$

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### Solution:

$\mathit{tan}4\theta =\frac{4\mathit{tan\theta }-4\mathit{ta}{n}^{3}\theta }{1-6\mathit{ta}{n}^{2}\theta +\mathit{ta}{n}^{4}\theta }$
Using the identity

$\frac{4\mathit{tan\theta }\left(1-\mathit{ta}{n}^{2}\theta \right)}{\left(1+\mathit{ta}{n}^{4}\theta -2\mathit{ta}{n}^{2}\theta -4\mathit{ta}{n}^{2}\theta \right)}$
$\frac{4\mathit{tan\theta }-4\mathit{ta}{n}^{3}\theta }{1-6\mathit{ta}{n}^{2}\theta +\mathit{ta}{n}^{4}\theta }$.
Type Exam: CBSE

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