Rút gọn biểu thức
\(A=\frac{sin2a+sin5a-sin3a}{1+cosa-2sin^22a}\)
\(A=\frac{sin2x+c\text{os}3x+sin6x+c\text{os}7x}{sin3x-s\text{inx}}\)
\(\frac{1+c\text{os}x-s\text{inx}}{1-c\text{os}x-s\text{inx}}=-cot\frac{x}{2}\)
Rút gọn các BT:
1) cos^2x+cos^2x.tan^2x
2) \(\frac{2cos^2a-1}{sina+cosa}\)
3) \(\frac{1-2sin^2a}{sina-cosa}\)
4) \(\frac{1+sina}{1-sina}-\frac{1-sina}{1+sina}\)
Rút gọn
a) A= \(\frac{4sin^2a}{1-cos^2\frac{a}{2}}\)
b) B= \(\frac{1+cosa-sina
}{1-cosa-sina}\)
c) C= \(\frac{1+sina-2sin^2\left(45-\frac{\pi}{2}\right)}{4cos\frac{a}{2}}\)
Chứng minh các đẳng thức sau:
a.\(\frac{1+sin^2x}{1-sin^{2^{ }}x}=1+2tan^2x\)
b.\(\frac{sin^3a-cos^3a}{sina-cosa}-sina.cosa=1\)
c.\(\frac{1+cosx+cos2x+cos3x}{2cos^2x+cosx-1}=2cosx\)
e.\(\frac{1-2sin^2a}{cosa+sina}+\frac{2cos^2a-1}{cosa-sina}=2cosa\)
d.\(\frac{1-cosx+cos2x}{sin2x-sinx}=cotx\)
MỌI NGƯỜI GIÚP MÌNH VỚI .MÌNH CẢM ƠN RẤT NHIỀU
Rút gọn các biểu thức :
A= \(\sqrt{3}\) sin ( x - \(\dfrac{\pi}{3}\) ) + sin ( x + \(\dfrac{\pi}{6}\) )
B= cos7x cos5x - \(\sqrt{3}\) sin2x + sin7x sin5x
C= 2sin( 2x -\(\dfrac{\pi}{6}\)) + 4sin + 1
D= \(\sqrt{3}\) cos2x + sin2x + 2sin(2x - \(\dfrac{\pi}{6}\))
E= sin2x + 2\(\sqrt{2}\) cosx + 2sin(x + \(\dfrac{\pi}{4}\)) +3
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: \(\frac{2tan\left(a+b\right)}{tana}=3\)
CMR
sin3x -2sin33x+cos2x.sinx=cos5x.sin4x
