Tính :
a, A = $cos12^{0}$ + $cos36^{0}$ + $cos60^{0}$ + $cos84^{0}$ + $cos96^{0}$ + $cos120^{0}$ + $cos144^{0}$ + $cos168^{0}$
b, B = cot$\frac{\pi}{9}$ x cot$\frac{2\pi}{9}$ x cot$\frac{5\pi}{18}$ x cot$\frac{7\pi}{18}$
Tính :
a, A = $cos12^{0}$ + $cos36^{0}$ + $cos60^{0}$ + $cos84^{0}$ + $cos96^{0}$ + $cos120^{0}$ + $cos144^{0}$ + $cos168^{0}$
b, B = cot$\frac{\pi}{9}$ x cot$\frac{2\pi}{9}$ x cot$\frac{5\pi}{18}$ x cot$\frac{7\pi}{18}$
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Đáp án:
$a) A = 0$
$b) B = 1$
Giải thích các bước giải:
$a)$
$A = cos12^0 + cos36^0 + cos60^0 + cos84^0 + cos96^0 + cos 120^0 + cos 144^0 + cos 168^0$
$= (cos 12^0 + cos 168^0) + (cos 36^0 + cos 144^0) + (cos60^0 + cos 120^0) + (cos 84^0 + cos 96^0)$
$= 0 + 0 + 0 + 0 = 0$
`\to A = 0`
$b)$
$B =$ `cot` `{\pi}/9 . cot` `{2\pi}/9 + cot` `{5\pi}/18 + cot` `{7\pi}/18`
$=$ `cot` `{\pi}/9 . cot` `{2\pi}/9 . cot (\pi/2 – {2\pi}/9) . cot (\pi/2 – \pi/9)`
$=$ `cot` `{\pi}/9 . cot` `+ {2\pi}/9 . tan` `{2\pi}/9 . tan` `{\pi}/9`
$=$ `cot` `{\pi}/9 . tan` `{\pi}/9 . cot` `{2\pi}/9 . tan` `{2\pi}/9`
$= 1.1 = 1$
`\to B = 1`
$\displaystyle \begin{array}{{>{\displaystyle}l}} cosa=-cos( \pi -a)\\ a.\ A=cos12^{o} +cos36^{o} +cos60^{o} +cos84^{o}\\ -cos12^{o} -cos36^{o} -cos60^{o} -cos84^{o} =0\\ tan\left(\frac{\pi }{2} -a\right) =cota\\ b.\ B=cot\frac{\pi }{9} .cos\frac{2\pi }{9} .tan\frac{2\pi }{9} .tan\frac{\pi }{9} =1 \end{array}$