tan(a+b)=(1/(17)) , tan(a−b)=((11)/(13)) tan2a=? tan2b=?


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Question Number 166170 by mathls last updated on 14/Feb/22

$t a n (a + b) = \frac{1}{17}, t a n (a - b) = \frac{11}{13}$ $t a n 2 a = ? t a n 2 b = ?$
	Answered by cortano1 last updated on 14/Feb/22

	$\Rightarrow 2 a = (a + b) + (a - b)$ $\Rightarrow \tan 2 a = \frac{\frac{1}{17} + \frac{11}{13}}{1 - \frac{1}{17} . \frac{11}{13}} = \frac{20}{21}$
	Commented by mathls last updated on 14/Feb/22

	$t h a n k s$
	Answered by cortano1 last updated on 14/Feb/22

	$\Rightarrow 2 b = (a + b) - (a - b)$ $\Rightarrow \tan 2 b = \frac{\frac{1}{17} - \frac{11}{13}}{1 + \frac{1}{17} . \frac{11}{13}} = - \frac{3}{4}$
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