1. lim_(a→−x) ((sin(x^2 − a^2 ))/(x^3 + a^3 )) = ? 2. cot 80° (tan 10° + 2 tg 70°) = ?


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Question Number 182200 by Shrinava last updated on 05/Dec/22

$1 . \lim_{a \to - x} \frac{\sin (x^{2} - a^{2})}{x^{3} + a^{3}} = ?$ $2 . \cot 80 ° (\tan 10 ° + 2 tg 70 °) = ?$
	Answered by cortano1 last updated on 06/Dec/22

	$1 . \lim_{a \to - x} \frac{\sin (x + a) (x - a)}{(x + a) (x^{2} - ax + a^{2})}$ $= \frac{2 x}{{3 x}^{2}} = \frac{2}{3 x}$
	Answered by som(math1967) last updated on 06/Dec/22

	$2 . t a n 80 = \frac{t a n 70 + t a n 10}{1 - t a n 70 t a n 10}$ $\Rightarrow t a n 80 - t a n 70 . t a n 10 . t a n 80$ $= t a n 70 + t a n 10$ $\Rightarrow t a n 80 - t a n 70 . t a n 10 . c o t 10$ $= t a n 70 + t a n 10$ $\Rightarrow t a n 80 - t a n 10 = 2 t a n 70$ $n o w c o t 80 (t a n 10 + 2 t a n 70)$ $= c o t 80 (t a n 10 + t a n 80 - t a n 10)$ $= c o t 80 \times t a n 80 = 1 a n s$
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