\(1-\frac{1}{4}sin^2x+cosx=1-\frac{1}{4}\left(1-cos^2x\right)+cosx\)
\(=\frac{3}{4}+\frac{1}{4}cos^2x+cosx=\frac{3}{4}+\frac{1}{4}\left(2cos^2\frac{x}{2}-1\right)^2+2cos^2\frac{x}{2}-1\)
\(=\frac{1}{4}\left(4cos^4\frac{x}{2}-4cos^2\frac{x}{2}+1\right)+2cos^2\frac{x}{2}-\frac{1}{4}\)
\(=cos^4\frac{x}{2}+cos^2\frac{x}{2}\)
Chứng minh các đẳng thức sau:
1/ \(sin^6\alpha+cos^6\alpha=\frac{5}{8}+\frac{3}{8}cos4\alpha\)
2/\(\frac{1+sin2\alpha-cos2\alpha}{1+cos2\alpha}=tan\alpha+tan^2\alpha\)
Chứng minh :
a) 2(1-sinx)(1+cosx) = (1-sinx+cosx)2
b) 1-cos2x/sin2x = tanx
c) 1+cotx+cot2x+cot3x = cosx+sinx/sin3x
Chứng minh VT=VP:
a) 2.(sinx+cosx+1)2.(sinx+cosx-1)2=1-cos4x
b) \(\frac{\text{3-4cos2a+cos4a}}{3+\text{4cos2a+cos4a}}\)= tan4a
c) (cos2x-sin2x)2+2(sin3x-sinx).cos-sin2x=cos2x
Cần GẤP ạ! Cảm ơn nhiều ạ!
Chứng minh|
a) \(\frac{1+sin2x}{sinx+cosx}-\frac{1-tan^2\frac{x}{2}}{1+tan^2\frac{x}{2}}=sinx\)
b) \(sin^4x+cos^4\left(x+\frac{\pi}{4}\right)=\frac{3}{4}-\frac{\sqrt{2}}{2}sin\left(2x+\frac{\pi}{4}\right)\)
1. sin^8(x) - cos^8(x) - 4sin^6(x) + 6sin^4(x) - 4sin^2(x) = 1
2. sin6x+sin4x+sin2x/1+cos2x+cos4x = 2sin2x
3. 1+sin2x /cosx+sinx - 1-tan^2(x/2)/1+tan^2(x/2) = sinx
4. cos4x + 4cos2x + 3 = 8cos^4(x)
5. 1+cosx+cos2x+cos3x/ 2cos^2(x)+cosx-1 = 2cosx
1. sin^8(x) - cos^8(x) - 4sin^6(x) + 6sin^4(x) - 4sin^2(x) = 1
2. sin6x+sin4x+sin2x/1+cos2x+cos4x = 2sin2x
3. 1+sin2x /cosx+sinx - 1-tan^2(x/2)/1+tan^2(x/2) = sinx
4. cos4x + 4cos2x + 3 = 8cos^4(x)
5. 1+cosx+cos2x+cos3x/ 2cos^2(x)+cosx-1 = 2cosx
a) chứng minh không phụ thuộc vào x
Q= [(1-sinx-cos2x+sin3x)/(cosx+sin2x+cos3x)]*tan(x-(pi/2)
b) chứng minh:
cos 5x*cos 3x+sin 7x*sin x=2cos^3 2x -2 cos^2 x +1
Chứng minh đẳng thức
\(2sin\left(\frac{\pi}{2}+x\right)+sin\left(3\pi-x\right)+sin\left(\frac{3\pi}{2}+x\right)+cos\left(\frac{\pi}{2}+x\right)=cosx\)
Bài 1 :Chứng minh đẳng thức :
a. \(\frac{1-2sin^2x}{1-tanx}=\frac{1+sin2x}{1+tanx}\)
b. \(\frac{cot^2\frac{x}{2}-cot^2\frac{3x}{2}}{cos^2\frac{x}{2}.cosx.\left(1+cot^2\frac{3x}{2}\right)}=8\)
Bài 2:Cho sin(2a+b) = 5sinb . CMR: \(\frac{2tan\left(a+b\right)}{tana}=3\)
