If tan 2θ tan θ = 1, then θ =


Question and Answers Forum

All Questions Topic List
UNKNOWN Questions
Previous in All Question Next in All Question
Previous in UNKNOWN Next in UNKNOWN
Question Number 62983 by hovea cw last updated on 27/Jun/19

$If \tan 2 θ \tan θ = 1, then θ =$
	Answered by Hope last updated on 27/Jun/19

	$t a n 2 θ = c o t θ = t a n (\frac{π}{2} - θ)$ $f o r m u l a$ $[t a n α = t a n β α = n π + β]$ $s o 2 θ = n π + (\frac{π}{2} - θ)$ $3 θ = \frac{(2 n + 1) π}{2} \to θ = \frac{(2 n + 1) π}{6}$
	Commented by mr W last updated on 27/Jun/19

	$p l e a s e c h e c k s i r!$ $n = 1 : θ = \frac{π}{2} \Rightarrow b u t \tan \frac{π}{2} \to \infty!$
	Commented by Hope last updated on 27/Jun/19

	$y e s s i r . . . y o u r r i g h t . . .$
	Answered by Hope last updated on 27/Jun/19

	$a n o t h d r w a y$ $a = t a n θ$ $\frac{2 a}{1 - a^{2}} \times a = 1$ $2 a^{2} = 1 - a^{2}$ $a^{2} = \frac{1}{3} \to a = \pm \frac{1}{\sqrt{3}}$ $t a n θ = t a n \frac{π}{6}$ $θ = n π + \frac{π}{6}$ $t a n θ = - \frac{1}{\sqrt{3}} = t a n (π - \frac{π}{6})$ $θ = n π + \frac{5 π}{6}$
	Commented by mr W last updated on 27/Jun/19

	$g o o d s i r!$ $t h a t i s θ = n π \pm \frac{π}{6}$
	Answered by MJS last updated on 27/Jun/19

	$\tan 2 θ = \frac{2 \sin θ \cos θ}{{2 \cos}^{2} θ - 1}$ $\frac{2 \sin θ \cos θ}{{2 \cos}^{2} θ - 1} \times \frac{\sin θ}{\cos θ} = 1$ $\frac{{2 \sin}^{2} θ}{{2 \cos}^{2} θ - 1} = 1$ $method 1$ ${2 \sin}^{2} θ = {2 \cos}^{2} θ - 1$ $\sin^{2} θ - \cos^{2} θ = - \frac{1}{2}$ $1 - {2 \cos}^{2} θ = - \frac{1}{2}$ $\cos^{2} θ = \frac{3}{4}$ $\cos θ = \pm \frac{\sqrt{3}}{2}$ $method 2$ $\frac{1 - \cos 2 θ}{\cos 2 θ} = 1$ $\cos 2 θ = \frac{1}{2}$ $. . .$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum