4tan18dg=...tan
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4tan18dg=...........tan
Cho M = tan 10◦ . tan 20◦ . tan 30◦ . tan 40◦ . tan 50◦ . tan 60◦ . tan 70◦ . tan 80◦ . Giá trị của M bằng.
gợi ý tan 10o = cot 80o
mà tan a . cot a =1
phần còn lại tự làm
chưa hiểu thì hỏi nhé
3,8 tan=tan
4,3 tan = tan
4,5 tan= tan
3 tháng 6 2020 lúc 19:55
Chứng minh với mọi tam giác không vuông ABC có:
a, tan A + tan B + tan C = tan A . tan B . tan C
b, tan 2A + tan 2B + tan 2C = tan 2A . tan 2B . tan 2C ( A, B, C ≠ \(\frac{\text{π}}{4}\) )
\(A+B+C=180^0\Rightarrow tan\left(A+B\right)=-tanC\)
\(\Rightarrow\frac{tanA+tanB}{1-tanA.tanB}=-tanC\Leftrightarrow tanA+tanB=-tanC+tanA.tanB.tanC\)
\(\Leftrightarrow tanA+tanB+tanC=tanA.tanB.tanC\)
\(2A+2B+2C=360^0\Rightarrow tan\left(2A+2B\right)=-tan2C\)
\(\Leftrightarrow\frac{tan2A+tan2B}{1-tan2A.tan2B}=-tan2C\)
\(\Leftrightarrow tan2A+tan2B+tan2C=tan2A.tan2B.tan2C\)
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\(\tan^210\times\tan^220\times\tan^230....\tan^260\times\tan^270\times\tan^280\)
12 tháng 4 2022 lúc 20:33
A+B+C=pi
chứng minh: tan(A/2).tan(B/2)+tan(B/2).tan(C/2)+tan(A/2).tan(C/2)=1
\(A+B+C=\pi\Rightarrow\dfrac{A}{2}+\dfrac{B}{2}=\dfrac{\pi}{2}-\dfrac{C}{2}\)
\(\Rightarrow tan\left(\dfrac{A}{2}+\dfrac{B}{2}\right)=tan\left(\dfrac{\pi}{2}-\dfrac{C}{2}\right)\)
\(\Rightarrow\dfrac{tan\dfrac{A}{2}+tan\dfrac{B}{2}}{1-tan\dfrac{A}{2}tan\dfrac{B}{2}}=cot\dfrac{C}{2}=\dfrac{1}{tan\dfrac{C}{2}}\)
\(\Rightarrow\left(tan\dfrac{A}{2}+tan\dfrac{B}{2}\right)tan\dfrac{C}{2}=1-tan\dfrac{A}{2}tan\dfrac{B}{2}\)
\(\Rightarrow tan\dfrac{A}{2}tan\dfrac{B}{2}+tan\dfrac{B}{2}tan\dfrac{C}{2}+tan\dfrac{C}{2}tan\dfrac{A}{2}=1\)
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Cho tam giác ABC.CMR:
tan(A/2)tan(B/2)+tan(B/2)tan(C/2)+tan(C/2)tan(A/2)=1
ta có: A\2+B\2 = π\2 - C\2
⇒ tan(A\2+B\2) = tan(π\2 -C\2)
⇒ (tanA\2 +tanB\2)\[1 - tanA\2.tanB\2] = cotgC\2
⇒ (tanA\2 +tanB\2).tanC\2 = [1 - tanA\2.tanB\2]
⇒ tanA\2.tanB\2 + tanB\2.tanC\2 + tanC\2.tanA\2 = 1
............đpcm............
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Giai các phương trình sau :
a/ tan 3x = tan x
b/ tan 3x + tan x = 0
c/ tan 2x - tan x = 0
d/ tan 2x + tan x = 0
HELP ME !!!!
a/ \(tan3x=tanx\Rightarrow3x=x+k\pi\Rightarrow2x=k\pi\Rightarrow x=\frac{k\pi}{2}\)
b/ \(tan3x+tanx=0\Rightarrow tan3x=-tanx=tan\left(\pi-x\right)\)
\(\Rightarrow3x=\pi-x+k\pi\Rightarrow4x=\pi+k\pi\Rightarrow x=\frac{\pi}{4}+\frac{k\pi}{4}\)
c/ \(tan2x-tanx=0\Rightarrow tan2x=tanx\)
\(\Rightarrow2x=x+k\pi\Rightarrow x=k\pi\)
d/ \(tan2x+tanx=0\Rightarrow tan2x=-tanx=tan\left(\pi-x\right)\)
\(\Rightarrow2x=\pi-x+k\pi\Rightarrow3x=\pi+k\pi\Rightarrow x=\frac{\pi}{3}+\frac{k\pi}{3}\)
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tan(100) x tan ( 200 ) x tan (300 ) x tan ( 400 ) x tan ( 500 ) x tan ( 600 ) x tan (700 ) x tan (800 )
\(tan10^0.tan80^0.tan20^0.tan70^0.tan30.tan60.tan40.tan50\)
\(=tan10.tan\left(90-10\right).tan20.tan\left(90-20\right).tan30.tan\left(90-30\right).tan40.tan\left(90-40\right)\)
\(=tan10.cot10.tan20.cot20.tan30.cot30.tan40.cot40\)
\(=1.1.1.1=1\)
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