Bạn nào giúp mình vs nhá:===thanks mọi người nhiều lắm^^
1/ cho tam giác ABC. cmr:
\(\dfrac{1}{sinA}+\dfrac{1}{sinB}+\dfrac{1}{sinC}=\dfrac{1}{2}.\left(tan\dfrac{A}{2}+tan\dfrac{B}{2}+tan\dfrac{C}{2}+cot\dfrac{A}{2}.cot\dfrac{B}{2}.cot\dfrac{C}{2}\right)\)
2,cmr:
\(\left(a-b\right)tan\dfrac{A}{2}.tan\dfrac{B}{2}+\left(b-c\right)tan\dfrac{B}{2}.tan\dfrac{C}{2}+\left(c-a\right)tan\dfrac{C}{2}.tan\dfrac{A}{2}=0\)
Cho A, B, C là 3 góc nhọn của tam giác ABC. Chứng minh:
a) \(tanA+tanB+tanC=tanA.tanB.tanC\)
Tính min P với \(P=tanA+tanB+tanC\)
b) \(tan\left(\dfrac{A}{2}\right).tan\left(\dfrac{B}{2}\right)+tan\left(\dfrac{B}{2}\right)tan\left(\dfrac{C}{2}\right)+tan\left(\dfrac{C}{2}\right).tan\left(\dfrac{A}{2}\right)=1\)
Tìm min T với \(T=tan\left(\dfrac{A}{2}\right)+tan\left(\dfrac{B}{2}\right)+tan\left(\dfrac{C}{2}\right)\)
Cho tam giác ABC , chứng minh rằng tan \(\left(\dfrac{B+C}{2}\right)\)= cot \(\dfrac{A}{2}\)
Cm biểu thức ko phụ thuộc x
\(A=\dfrac{cot^2a-cos^2a}{cot^2a}+\dfrac{sinacosa}{cota}\)
A= sin8x+\(2cos^2x\left(4x+\dfrac{\pi}{4}\right)\)
Cm đẳng thức
\(\dfrac{sin2a-2sina}{sin2a+2sina}+tan^2\dfrac{a}{2}=0\)
\(\dfrac{sina}{1+cosa}+\dfrac{1+cosa}{sina}=\dfrac{2}{sina}\)
\(\dfrac{sin^2x}{sinx-cosx}-\dfrac{sinx+cosx}{tan^2x-1}=sinx+cosx\)
\(\dfrac{sin\left(a+b\right)sin\left(a-b\right)}{1-tan^2a.cot^2b}=-cos^2a.sin^2b\)
C\m các đẳng thức sau :...........................................................Giúp Mình Với ...
a, \(\sin^2\left(\dfrac{A}{2}\right)+\sin^2\left(\dfrac{B}{2}\right)+\sin^2\left(\dfrac{C}{2}\right)=1+2\sin\left(\dfrac{A}{2}\right)\sin\left(\dfrac{B}{2}\right)\sin\left(\dfrac{C}{2}\right)\)
b. \(\tan\left(\dfrac{A}{2}\right)\tan\left(\dfrac{B}{2}\right)+\tan\left(\dfrac{B}{2}\right)\tan\left(\dfrac{C}{2}\right)+\tan\left(\dfrac{C}{2}\right)\tan\left(\dfrac{A}{2}\right)=1\)
Tính giá trị biểu thức:
\(P=\left[Tan\dfrac{17\Pi}{4}+Tan\left(\dfrac{7\Pi}{2}-x\right)\right]^2+\left[Cot\dfrac{13\Pi}{4}+Cot\left(7\Pi-x\right)\right]^2\)
Cho \(sina=\dfrac{3}{5},cosb=-\dfrac{5}{13}\)và \(\dfrac{\pi}{2}< a,b< \pi\)
Tính \(cos\dfrac{a}{2};sin\dfrac{b}{2};tan\left(a+b\right);sin\left(a-b\right)\)
GIÚP VỚI MÌNH ĐANG CẦN GẤP
Chứng minh các đẳng thức sau:
a, \(\sin^4\alpha-\cos^4\alpha+1=2\sin^2\alpha\)
b,\(\dfrac{\sin^2\alpha+2\cos^2\alpha-1}{\cot^2\alpha}=\sin^2\alpha\)
c, \(\dfrac{1-\sin^2\alpha.\cos^2\alpha}{\cos^2\alpha}-\cos^2\alpha=\tan^2\alpha\)
d, \(\dfrac{\sin^2\alpha-\tan^2\alpha}{\cos^2\alpha-\cot^2\alpha}=\tan^6\alpha\)
e, \(\left(1+\cot\alpha\right)\sin^3\alpha+\left(1+\tan\alpha\right)\cos^3\alpha=\sin\alpha.\cos\alpha\)
f,\(\dfrac{\left(\sin\alpha+\cos\alpha\right)^2-1}{\cot\alpha-\sin\alpha.\cos\alpha}=2\tan^2\alpha\)
Đơn giản các biểu thức sau:
G = \(cos\left(\alpha-5\pi\right)+sin\left(-\dfrac{3\pi}{2}+\alpha\right)-tan\left(\dfrac{\pi}{2}+\alpha\right).cot\left(\dfrac{3\pi}{2}-\alpha\right)\)
H = \(cot\left(\alpha-2\pi\right).cos\left(\alpha-\dfrac{3\pi}{2}\right)+cos\left(\alpha-6\pi\right)-2sin\left(\alpha-\pi\right)\)
Rút gọn các biểu thức sau
1, \(\dfrac{1+\cot x}{1-\cot x}-\dfrac{2+2\cot^2x}{\left(\tan x-1\right)\left(\tan^2x+1\right)}\)
2, \(\sqrt{\sin^4x+6\cos^2x+3\cos^4x}+\sqrt{\cos^4x+6\sin^2x+3\sin^4x}\)
