tan (x+y)= ((12)/5) sin (x−y) = (3/5) x+y , x−y are acute angles . tan x tan y = ?


Question and Answers Forum

All Questions Topic List
None Questions
Previous in All Question Next in All Question
Previous in None Next in None
Question Number 141423 by naka3546 last updated on 18/May/21

$\tan (x + y) = \frac{12}{5}$ $\sin (x - y) = \frac{3}{5}$ $x + y, x - y a r e a c u t e a n g l e s .$ $\tan x \tan y = ?$
	Answered by mr W last updated on 18/May/21

	$u = \tan x, v = \tan y$ $\frac{u + v}{1 - u v} = \frac{12}{5} \Rightarrow u + v = \frac{12 (1 - u v)}{5}$ $\tan (x - y) = \frac{3}{4}$ $\frac{u - v}{1 + u v} = \frac{3}{4} \Rightarrow u - v = \frac{3 (1 + u v)}{4}$ $u = \frac{1}{2} (\frac{12 (1 - u v)}{5} + \frac{3 (1 + u v)}{4}) = \frac{63 - 33 u v}{40}$ $u = \frac{1}{2} (\frac{12 (1 - u v)}{5} - \frac{3 (1 + u v)}{4}) = \frac{33 - 63 u v}{40}$ $u v = \frac{63 - 33 u v}{40} \times \frac{33 - 63 u v}{40}$ $2079 {(u v)}^{2} - 6658 (u v) + 2079 = 0$ $u v = \frac{3329 \pm 2600}{2079} = \frac{77}{27} o r \frac{27}{77}$
	Commented by naka3546 last updated on 25/May/21

	$Thank you, sir .$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum