Giải PT
a) \(\left|\sin x-\cos x\right|+\left|\sin x+\cos x\right|=2\)
b) \(\tan x-3\cot x=4\left(\sin x+\sqrt{3}\cos x\right)\)
c) \(2\sin^2x-2\sqrt{2}\sin x+3\tan^22x-2\sqrt{3}\tan2x+2=0\)
giải phương trình
\(\sin x\sqrt{1+2\sin x}=\cos2x\)
\(\sin\left(\frac{5x}{2}-\frac{\pi}{4}\right)-\cos\left(\frac{x}{2}-\frac{\pi}{4}\right)=\sqrt{2}\cos\frac{3x}{2}\)
\(3\sqrt{\tan x+1}\left(\sin x+2\cos x\right)=5\left(\sin x+3\cos x\right)\)
\(\sqrt{2}\left(\sin x+\sqrt{3}\cos x\right)=\sqrt{3}\cos2x-\sin2x\)
\(\sin2x\sin4x+2\left(3\sin x-4\sin^2x+1\right)=0\)
giải phương trình
a, \(2\sin\frac{x}{2}\left(\sin\frac{3x}{2}+\cos\frac{3x}{2}\right)=3-4\cos x\)
b, \(\frac{2\cos^2x+\sqrt{3}\sin2x+3}{2\cos^2x.\sin\left(x+\frac{\pi}{3}\right)}=3\left(\tan^2x+1\right)\)
\(\sin x\left(1+\tan x.\tan\frac{x}{2}\right)+\tan x+2\sqrt{3}=\frac{\sqrt{3}}{\cos^2x}\)
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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Giải PT
a1) \(3.\cos4x-2^{ }\cos^23x=1\)
a2) \(2\cos2x-8\cos x+7=\dfrac{1}{\cos x}\)
a3) \(\dfrac{\left(1+\sin x+\cos2x\right)\sin\left(x+\dfrac{\pi}{4}\right)}{1+\tan x}=\dfrac{1}{\sqrt{2}}\cos x\)
a4) \(9\sin x+6\cos x-3\sin2x+\cos2x=8\)
Giải phương trình : \(\tan x.\cot2x=\left(1+\sin x\right)\left(4\cos^2x+\sin x-5\right)\)
Tìm tập xác định của y=f(x)=\(\dfrac{\sin\left(3x\right)}{\tan^2\left(x\right)-1}+\sqrt{\dfrac{2-\cos\left(x\right)}{1+\cos\left(x\right)}}\)
a)\(\sin^22x+\sqrt{3}\sin4x+3\cos^22x=0\)
b)\(\sqrt{2}\left(\sin x+\cos x\right)=\tan x+\cot x\)
