giai cac pt
a) \(sin^3\left(x+\frac{\pi}{4}\right)=\sqrt{2}sinx\)
b) \(cos^3x-sin^3x=\sqrt{2}cos\left(x-\frac{\pi}{4}\right)\)
c) \(\frac{1-tanx}{1+tanx}=1+2sinx\)
d) \(\left(1+tanx\right)sin^2x=3sinx\left(cosx-sinx\right)+3\)
giai pt
a) \(cos^3x-sin^3x=\sqrt{2}cos\left(x-\frac{\pi}{4}\right)\)
b) \(\frac{1-tanx}{1+tanx}=1+2sinx\)
c) \(\left(1+tanx\right)sin^2x=3sinx\left(cosx-sinx\right)+3\)
giải phương trình
a, \(2\sin\frac{x}{2}\left(\sin\frac{3x}{2}+\cos\frac{3x}{2}\right)=3-4\cos x\)
b, \(\frac{2\cos^2x+\sqrt{3}\sin2x+3}{2\cos^2x.\sin\left(x+\frac{\pi}{3}\right)}=3\left(\tan^2x+1\right)\)
\(\sin x\left(1+\tan x.\tan\frac{x}{2}\right)+\tan x+2\sqrt{3}=\frac{\sqrt{3}}{\cos^2x}\)
giải các pt
a) \(tanx+tan\left(\frac{2\pi}{3}-3x\right)=0\)
b) \(tan\left(2x-15^o\right)-tanx=0\)
c) \(\frac{tan2x-2}{2tan2x+1}=3\)
d) \(\frac{sinx+\sqrt{3}cosx}{3sinx-\sqrt{3}cosx}=1\)
Bài 1:
a) 4sin23x + 2(\(\sqrt{3}\)+1) cos 3x - \(\sqrt{3}\)= 4
b) cos2x + 9cosx + 5 = 0
c) 4cos5(2 - 6x) + 16cos2(1 - 3x) =13
d)\(\frac{1}{cos^2x}-\left(3+\sqrt{3}\right)tanx-3+\sqrt{3}=0\)
e) \(\frac{3}{cosx}+tan^2x=9\)
f) 9 - 13cosx + \(\frac{4}{1+tan^2x}=0\)
g) \(\frac{1}{sin^2x}=cotx+3\)
h) \(\frac{1}{cos^2x}+3cot^2x=5\)
i) cos2x - 3cosx = 4cos2\(\frac{x}{2}\)
k) 2cos2x + tanx=\(\frac{4}{5}\)
giải các pt
a) \(\frac{tanx-8\sqrt{3}}{tanx-2\sqrt{3}}=3\)
b) \(tan2x+cot\frac{5\pi}{8}=0\)
c) \(\sqrt{3}tan\left(\frac{\pi}{9}-2x\right)+3=0\)
d) \(\left(tanx-5\right)\left(tan4-tan2x\right)=0\)
Tìm TXĐ
1. y=\(\frac{cotx}{1-sinx}\)
2.y=\(\frac{1+tan\left(2x+\frac{\pi}{3}\right)}{cot^{2^{ }}x+1}\)
3.y=\(\sqrt{\frac{5-3cos2x}{1+sin\left(2x-\frac{\pi}{2}\right)}}\)
4.y=\(\frac{1+cot\left(x+\frac{\pi}{3}\right)}{tan^2\left(3x-\frac{\pi}{4}\right)}\)
giải các pt
a) \(3cos4x-8cos^6x+2cos^2x+3=0\)
b) \(4+3sinx+sin^3x=3cos^2x+cos^6x\)
c) \(2cos^2x\left(1+tanx.tan\frac{x}{2}\right)=cos2x-3\)
d) \(\frac{\sqrt{3}}{cos^2x}-tanx-2\sqrt{3}=sinx\left(1+tanx.tan\frac{x}{2}\right)\)