\(32cos^6\left(\dfrac{x}{2}\right)+3sinx-4sin^3x=3sinx\)
\(\Leftrightarrow\left(2cos^2\dfrac{x}{2}\right)^3=sin^3x\)
\(\Leftrightarrow2cos^2\dfrac{x}{2}=sinx\)
\(\Leftrightarrow cosx+1=sinx\)
\(\Leftrightarrow sinx-cosx=1\)
\(\Leftrightarrow\sqrt{2}sin\left(x-\dfrac{\pi}{4}\right)=1\)
\(\Leftrightarrow...\)
Giải pt
\(32\sin^6\dfrac{x}{2}+\sin3x=3\sin x\)
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/\(4\sin2x=\dfrac{\cos^2x-\sin^2x}{\cos^6x+\sin^6x}\)
mọi người giải giúp em với em đang cần gấp ạ
Xét tính chẵn, lẻ của các hàm số
1,\(y=cosx+sin^2x\)
2,\(y=sinx+cosx\)
3,\(y=tanx+2sinx\)
4,\(y=tan2x-sin3x\)
5,\(sin2x+cosx\)
6,\(y=cosx.sin^2x-tan^2x\)
7,\(y=cos\left(x-\dfrac{\pi}{4}\right)+cos\left(x+\dfrac{\pi}{4}\right)\)
8,\(y=\dfrac{2+cosx}{1+sin^2x}\)
9,\(y=\left|2+sinx\right|+\left|2-sinx\right|\)
Giải pt: \(\sin3x+\cos3x-2\sqrt{2}\cos\left(x+\dfrac{\pi}{4}\right)+1=0\)
Tìm nghiệm của các phương trinh:
1,\(\left(sinx+\dfrac{sin3x+cos3x}{1+2sin2x}\right)=\dfrac{3+cos2x}{5}\)
2,\(48-\dfrac{1}{cos^4x}-\dfrac{2}{sin^2x}\left(1+cot2xcotx\right)=0\)
3,\(cos^4x+sin^4x+cos\left(x-\dfrac{\pi}{4}\right)sin\left(3x-\dfrac{\pi}{4}\right)-\dfrac{3}{2}=0\)
4,\(cos5x+cos2x+2sin3xsin2x=0\) trên \(\left[0;2\pi\right]\)
5,\(\dfrac{cos\left(cosx+2sinx\right)+3sinx\left(sinx+\sqrt{2}\right)}{sin2x-1}=1\)
6,\(\left(sinx+\dfrac{sin3x+cos3x}{1+2sin2x}\right)=\dfrac{3+cos2x}{5}\)
7,\(cos\left(2x+\dfrac{\pi}{4}\right)+cos\left(2x-\dfrac{\pi}{4}\right)+4sinx=2+\sqrt{2}\left(1-sinx\right)\)
Giai các pt sau
1. \(\sqrt{3}\cos5x-2\sin3x.\cos2x-\sin x=0\)
4. \(\sin3x+\cos3x-\sin x+\cos x=\sqrt{2}\cos2x\)
6. \(\sin x+\cos x.\sin2x+\sqrt{3}\cos3x=2\left(\cos4x+\sin x^3\right)\)
1) cos3x - cos4x + cos5x =0
2) sin3x + cos2x = 1 + 2sinx.cos2x
3) cos2x - cosx = 2 sin\(^2\)\(\dfrac{3x}{2}\)
4) cos\(^2\)2x + cos\(^2\)3x = sin\(^2\)x
5) sin3x.sin5x - cos4x.cos6x = 0
giải pt
a, \(\sin^2x+\sin^22x+\sin^23x=\dfrac{3}{2}\)
b. \(\cos^2x+\sin^22x+\cos^23x=1\)
c,\(\sin5x+2\cos^2x=1\)
d,\(1+\tan x=2\sqrt{2}\sin\left(x+\dfrac{\pi}{4}\right)\)
e,\(\sin3x+\cos3x-\sin x+\cos x=\sqrt{2}\cos2x\)
sin3x -2cos2x = 3sinx +2cosx
Giai pt sau :
a)sin^2 x - 3sinx - 4 = 0
b)√3sinx + cos = 2sin 2x
