tan(π/(12))=((sinα−sin(π/(12)))/(cosα+cos(π/(12)))) α=?


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Question Number 197944 by liuxinnan last updated on 05/Oct/23

$t a n \frac{π}{12} = \frac{s i n α - s i n \frac{π}{12}}{c o s α + c o s \frac{π}{12}}$ $α = ?$
	Answered by MM42 last updated on 05/Oct/23

	$s i n \frac{π}{12} \times c o s α + s i n \frac{π}{12} \times c o s \frac{π}{12} = s i n α \times c o s \frac{π}{12} - s i n \frac{π}{12} \times c o s \frac{π}{12}$ $\Rightarrow s i n (α - \frac{π}{12}) = 2 s i n \frac{π}{12} \times c o s \frac{π}{12} = s i n \frac{π}{6}$ $\Rightarrow {\begin{cases} α = 2 k π + \frac{π}{4} ✓ \\ α = 2 k π + \frac{11 π}{12} \times \end{cases}$
	Commented by MM42 last updated on 05/Oct/23
	$Sir “W” in the denominator of the fraction is written “ cosα+cos(π/(12)) ”$
	$S i r ‘ ‘ W^{″}$ $i n t h e d e n o m i n a t o r o f t h e f r a c t i o n$ $i s w r i t t e n ‘ ‘ c o s α + c o s \frac{π}{12}^{″}$
	Commented by mr W last updated on 06/Oct/23

	$y e s . i n o t i c e d i t a l s o, b u t t o o l a t e .$
	Commented by MM42 last updated on 06/Oct/23

	$⋚ \underset{⏟}{M}$
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