tan-pi-12-sin-sin-pi-12-cos-cos-pi-12-

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

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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