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Precalculus Mathematics Homework Help
Angle between two straight lines
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[QUOTE="arpon, post: 5415764, member: 526026"] [h2]Homework Statement [/h2] Find the angle between the straight lines: ##(x^2+y^2)(\cos^2{\theta} \sin^2{\alpha} + \sin^2{\theta})=(x \tan{\theta} - y \sin{\alpha})^2## [h2]Homework Equations[/h2] [Not applicable] [h2]The Attempt at a Solution[/h2] Dividing by ##x^2##, ## (1+(\frac{y}{x})^2)(\cos^2{\theta} \sin^2{\alpha} + \sin^2{\theta})=(\tan{\theta} - \frac{y}{x} \sin{\alpha})^2 ## Let, ##\frac{y}{x} =m ##. ## (1+m^2)(\cos^2{\theta} \sin^2{\alpha} + \sin^2{\theta})=(\tan{\theta} - m \sin{\alpha})^2 ## ##(\sin^2{\theta} \cos^2{\alpha}) m^2 + (2 \tan{\theta} \sin{\alpha}) m + (\cos^2{\theta} \sin^2{\alpha} + \sin^2{\theta}-\tan^2{\theta}) = 0 ## So the solutions of this equation indicate the slopes of the two straight lines. If the solutions are ##m_1## and ##m_2##, then the angle between the two straight lines will be ##\arctan{\frac{m_1-m_2}{1+m_1 m_2}}##; I came up with a messy equation, as I tried to calculate this. But the answer is very simple, just ##2\theta##. So, I think there is some clever technique to solve this problem. Any suggestion will be appreciated [/QUOTE]
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Precalculus Mathematics Homework Help
Angle between two straight lines
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