Tuyển Cộng tác viên Hoc24 nhiệm kì 26 tại đây: https://forms.gle/dK3zGK3LHFrgvTkJ6
c/m\(\frac{1-\cos x+\sin2x}{\sin2x-\sin x}=\cot x\)
\(A=\left(\tan x+\cot x\right)^2-\left(\tan x-\cot x\right)^2\)
\(B=\sin^6x+\cos^6x+3\sin^2x+\cos^2x\)
CMR: cos x/(sin x - cos x) + Sin x/(sin x + cos x) = (1+cot^2 x)/(1-cot^2 x)
giải pt
a) \(\sin^2\left(\frac{x}{2}-\frac{\pi}{4}\right).tan^2x-cos^2\frac{x}{2}=0\)
b) \(3tan^3x-tanx+\frac{3\left(1+sinx\right)}{cos^2x}-8cos^2\left(\frac{\pi}{4}-\frac{x}{2}\right)=0\)
giải pt sau :
\(\left(cos\frac{x}{4}-3sinx\right).sinx+\left(1+sin\frac{x}{4}-3cosx\right).cosx=0\)
RÚT GỌN:
1. \(4\sin xsin\left(x+\frac{\pi}{2}\right)sin\left(2x+\frac{\pi}{2}\right)\)
2 \(1-8\sin^2x\cos^2x\)
3 \(\frac{2}{\left(1-\tan a\right)\left(1+\cot a\right)}\)
4 \(\left(1-\tan^2a\right)\cot a\)
5 \(\cos^2\frac{\pi}{24}-\cos^4\frac{\pi}{24}\)
Chứng minh
a)\(\left(\sin x+\cos x\right)^2=1+2\sin x\)\(\cos x\)
b)\(\left(\sin x+\cos x\right)^2+\left(\sin x-\cos x\right)^2=2\)
c)\(\sin^4x+\cos^4x=1-2\sin^2x\cos^2x\)
\(\sin2x+\sqrt{3}\cos2x+\left(2+\sqrt{3}\right)\sin x-\cos x=1+\sqrt{3}\)
CMR: \(\frac{\sin^2\alpha}{\cos\alpha\left(1+\tan\alpha\right)}-\frac{\cos^2\alpha}{\sin\alpha\left(1+\cot\alpha\right)}=\sin\alpha-\cos\alpha\)
