\(\Leftrightarrow\left(2\sin x-1\right)\left(\cos x+\sin x+1\right)=0\)
\(\Leftrightarrow\begin{cases}\sin x=\frac{1}{2}\\\sin x+\cos x=-1\end{cases}\)
\(\Leftrightarrow\left[x=\frac{\pi}{6}+k2\pi;x=\frac{5\pi}{6}+k2\pi;x=-\frac{\pi}{2}+k2\pi;x=\pi+k2\pi\right]\)
giai pt:
a) \(4sin^5x.cosx-4cos^5x.sinx=sin^24x\)
b) \(4sin^2\frac{x}{2}-\sqrt{3}cos2x=1+2cos^2\left(x-\frac{3\pi}{4}\right)\)
c) \(sin^2\left(x+\frac{\pi}{3}\right)+sinx+\sqrt{3}cosx=\frac{5}{4}\)
d) \(2sinx\left(1+cos2x\right)+sin2x=1+2cosx\)
e) \(sin^2x+4sinx.cosx+3cos^2x-sinx-3ccosx=0\)
giải pt
a) \(\sqrt{3}sinx+cosx=2\)
b) \(sin\left(\frac{\pi}{4}-2x\right)+sin\left(\frac{\pi}{4}+x\right)=\frac{\sqrt{2}}{2}\)
Biến đổi về phương trình gồm sin và cos ( bậc 1 ) :
a ) \(4\sin^2\frac{x}{2}-\sqrt{3}\cos2x=1+2\cos^2\left(x-\frac{3\pi}{4}\right)\)
b) \(9\sin x+6\cos x-3\sin2x+\cos2x=8\)
GPT
a) \(sin\left(2x+1\right)+cos\left(3x-1\right)=0\)
b) \(sin\left(2x-\frac{\pi}{6}\right)=-sin\left(x-\frac{\pi}{4}\right)\)
c) \(sin\left(3x+\frac{2\pi}{3}\right)+sin\left(x-\frac{7\pi}{5}\right)=0\)
d) \(cos\left(4x+\frac{\pi}{3}\right)+sin\left(x-\frac{\pi}{4}\right)=0\)
tìm TXĐ
1.y=\(\frac{1}{\sin x}+\frac{1}{\cos x}\)
2.y=\(\sqrt{3-\sin x}\)
3.y=\(\sqrt{\frac{\sin^2x}{1+\sin x}}\)
4.y=\(\tan\left(2x-\frac{\Pi}{4}\right)\)
GPT
a) \(sin2x-cosx=0\)
b) \(\left(2cos\frac{x}{2}-1\right)\left(sin\frac{x}{2}+2\right)=0\)
c) \(\left(\sqrt{3}tanx+1\right)\left(sin^2x+1\right)=0\)
d) \(sinx.cosx.cos2x=0\)
e) \(8cos2x.sin2x.cos4x=-\sqrt{2}\)
giai pt
a) \(sin^6x+cos^6x+sin2x=1\)
b) \(1+sinx+cosx+sin2x+cos2x=0\)
c) \(sin^2x-3cos^2x=2\left(sinx+\sqrt{3}cosx\right)\)
d) \(sin^3x.cosx-sinx.cos^3x=\frac{\sqrt{2}}{8}\)
từ pt \(1+sin^3x+cos^3x=\frac{3}{2}sin2x\). tính \(cos\left(x+\frac{\pi}{4}\right)\)
BT1: Tìm GTNN, GTLN
a) \(A=\sin^2x-2\sin x+2\)
b) \(B=-2\sin^2x+4\sin2x+1\)
BT2: Xác định tính chẵn lẻ
a) \(A=\dfrac{\left|\sin x\right|}{\sin^2x+1}\)
b) \(B=\dfrac{Sinx}{\left|Sin2x\right|+1}\)
c) \(C=\dfrac{Sin^32x}{Sin^4x+4}\)
