\(=\frac{1+cosx}{sinx}\left(1-\frac{1+cos^2x-2cosx}{sin^2x}\right)=\frac{1+cosx}{sinx}\left(\frac{sin^2x-1-cos^2x+2cosx}{sin^2x}\right)\)
\(=\frac{1+cosx}{sinx}\left(\frac{-cos^2x-cos^2x+2cosx}{sin^2x}\right)=\frac{\left(1+cosx\right)2cosx\left(1-cosx\right)}{sinx.sin^2x}\)
\(=\frac{2cosx\left(1-cos^2x\right)}{sinx.sin^2x}=\frac{2cosx.sin^2x}{sinx.sin^2x}=\frac{2cosx}{sinx}=2cotx\)
Rút gọn các biểu thức sau
1, \(\dfrac{1+\cot x}{1-\cot x}-\dfrac{2+2\cot^2x}{\left(\tan x-1\right)\left(\tan^2x+1\right)}\)
2, \(\sqrt{\sin^4x+6\cos^2x+3\cos^4x}+\sqrt{\cos^4x+6\sin^2x+3\sin^4x}\)
Rút gọn A=\(\frac{1+\cos x}{\sin x}\left[1-\frac{\left(1-\cos x\right)^2}{sin^2x}\right]\)
AI LÀM ĐƯỢC SẼ ĐC 1 TICK
chứng minh các đẳng thức sau
a) \(\tan^2x-\sin^2x=\tan^2x.\sin^2x\)
b) \(\tan x+\cot x=\frac{1}{\sin x.\cot x}\)
c) \(\frac{1-\cos x}{\sin x}=\frac{\sin x}{1+\cos x}\)
d) \(\frac{1}{1+\tan x}+\frac{1}{1+\cot x}=1\)
e) \(\left(1-\frac{1}{\cos x}\right)\left(1+\frac{1}{\cos x}\right)+\tan^2x=0\)
Rút gọn các biểu thức sau:
1) \(A=2cosx+3cosx\left(\pi-x\right)-sin\left(\frac{7\pi}{2}-x\right)+tan\left(\frac{3\pi}{2}-x\right)\)
2) \(B=2sin\left(\frac{\pi}{2}+x\right)+sin\left(5\pi-x\right)+sin\left(\frac{3\pi}{2}+x\right)+cos\left(\frac{\pi}{2}+x\right)\)
Chứng minh rằng: (Pls help me)
a, \(\frac{1}{\sin x}+\cot x=\cot\frac{x}{2}\)
b, \(\frac{1-\cos x}{\sin x}=\tan\frac{x}{2}\)
c,\(\tan\frac{x}{2}\left(\frac{1}{\cos x}+1\right)=\tan x\)
d,\(\frac{\sin2a}{2\cos a\left(1+\cos a\right)}=\tan\frac{a}{2}\)
e,\(\cot x+\tan\frac{x}{2}=\frac{1}{\sin x}\)
f,\(3-4\cos2x+\cos4x=8\sin^4x\)
g,\(\frac{1-\cos x}{\sin x}=\frac{\sin x}{1+\cos x}\)
h,\(\sin x+\cos x=\sqrt{2}\sin\left(x+\frac{\pi}{4}\right)\)
i,\(\sin x-\cos x=\sqrt{2}\sin\left(x-\frac{\pi}{4}\right)\)
l,\(\cos x-\sin x=\sqrt{2}\cos\left(x+\frac{\pi}{4}\right)\)
chứng minh các đẳng thức sau
a) \(\cos x\cos\left(\frac{\pi}{3}-x\right)\cos\left(\frac{\pi}{3}+x\right)=\frac{1}{4}\cos3x\)
b) \(\sin5x-2\sin x\left(\cos4x+\cos2x\right)=\sin x\)
Thu gọn biểu thức
\(A=sin\left(\pi+x\right)-cos\left(\frac{\pi}{2}-x\right)+cot\left(2\pi-x\right)\)
1) Rút gọn biểu thức :
\(M=2\left(sin^4x+cos^4x+cos^2.sin^2x\right)^2-\left(sin^8x+cos^8x\right)\)
giải phương trình:
\(\frac{\cos x\left(\cos x+2\sin x\right)+3\sin x\left(\sin x+\sqrt{2}\right)}{2\sin x-1}=1\)
