Cho tam giác ABC; AB = c; AC = b; BC = a; đường phân giác AD. Chứng minh:

1) \(\sin\dfrac{A}{2}\le\dfrac{a}{b+c}\)

2) \(\sin\dfrac{A}{2}+\sin\dfrac{B}{2}+\sin\dfrac{C}{S}< 2\)

3) \(\dfrac{1}{\sin\dfrac{A}{2}}+\dfrac{1}{\sin\dfrac{B}{2}}+\dfrac{1}{\sin\dfrac{C}{2}}\ge6\)

4) \(\sin\dfrac{A}{2}+\sin\dfrac{B}{2}+\sin\dfrac{C}{2}\le\dfrac{1}{8}\)

5) \(\dfrac{1}{\sin^2\dfrac{A}{2}}+\dfrac{1}{\sin^2\dfrac{B}{2}}+\dfrac{1}{\sin^2\dfrac{C}{2}}\ge12\)

Cho A, B, C là 3 góc trong tam giác. Chứng minh rằng:

1, sin A + sin B - sin C = 4sin\(\dfrac{A}{2}\) sin \(\dfrac{B}{2}\)sin \(\dfrac{C}{2}\)

2, \(\dfrac{sinA+sinB-sinC}{cosA+cosB-cosC+1}=tan\dfrac{A}{2}tan\dfrac{B}{2}tan\dfrac{C}{2}\) (ΔABC nhọn)

3, \(\dfrac{cosA+cosB+cosC+3}{sinA+sinB+sinC}=tan\dfrac{A}{2}+tan\dfrac{B}{2}+tan\dfrac{C}{2}\)

GIÚP MÌNH VỚI!!!

a/\(\sin3x+\cos2x=1+2\sin x\cos2x\)

b/\(\sin^3x+\cos^3x=2\left(\sin^5x+\cos^5x\right)\)

c/\(\dfrac{\tan x}{\sin x}-\dfrac{\sin x}{\cos x}=\dfrac{\sqrt{2}}{2}\)

d/\(\dfrac{\cos x\left(\cos x+2\sin x\right)+3\sin x\left(\sin x+\sqrt{2}\right)}{\sin2x-1}=1\)

e/\(\sin^2x+\sin^23x-2\cos^22x=0\)

f/\(\dfrac{\tan x-\sin x}{\sin^3x}=\dfrac{1}{\cos x}\)

g/\(\sin2x\left(\cos x+\tan2x\right)=4\cos^2x\)

h/\(\sin^2x+\sin^23x=\cos^2x+\cos^23x\)

k/\(4\sin2x=\dfrac{\cos^2x-\sin^2x}{\cos^6x+\sin^6x}\)

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