\(sinx+cosx=\frac{1}{5}\Rightarrow\left(sinx+cosx\right)^2=\frac{1}{25}\)
\(\Rightarrow1+2sinx.cosx=\frac{1}{25}\Rightarrow2sinx.cosx=-\frac{24}{25}\)
\(\Rightarrow4sinx.cosx=-\frac{48}{25}\)
\(\Rightarrow\left(sinx+cosx\right)^2-4sinx.cosx=\frac{1}{25}+\frac{48}{25}=\frac{49}{25}\)
\(\Rightarrow\left(sinx-cosx\right)^2=\frac{49}{25}\Rightarrow\left|sinx-cosx\right|=\frac{7}{5}\)
Chứng minh đẳng thức sau :
a, \(\left(\frac{tan^2x-1}{2tanx}\right)^2\) - \(\frac{1}{4sin^2x.cos^2x}\) = -1
b, \(\frac{cos^2x-sin^2x}{sin^4x+cos^4x-sin^2x}\) = 1 + tan2x
c, \(\frac{sin^2x}{cosx.\left(1+tanx\right)}-\frac{cos^2x}{sinx.\left(1+cotx\right)}=sinx-cosx\)
d, \(\left(\frac{cosx}{1+sinx}+tanx\right).\left(\frac{sinx}{1+cosx}+cotx\right)=\frac{1}{sinx.cosx}\)
e, cos2x.(cos2x + 2sin2x + sin2x.tan2x) = 1
Chứng minh đẳng thức lượng giác
câu 1) sin(\(\frac{\text{π}}{2}\)-α)cos(π-α) = \(\frac{-1}{1+tan^2\left(\text{π}-\text{α}\right)}\)
Câu 2) sin2 (\(\frac{\text{π}}{2}\)-α)= \(\frac{1}{1+tan^2}\)
Câu3) sin6\(\frac{x}{2}\) - cos6\(\frac{x}{2}\)=\(\frac{1}{4}\) cos x (sin2x -4)
Câu 4) \(\frac{1-sin^2x}{2cot\left(\frac{\text{π}}{4}+x\right).cot^2\left(\left(\frac{\text{π}}{4}-x\right)\right)}\)
Rút gọn biểu thức
A=\(\frac{2Sina-Sin4a}{2Sina+Sin4a}\)
B=\(\frac{Sin\left(\frac{\pi}{4}-a\right)+Cos\left(\frac{\pi}{4}-a\right)}{Sin\left(\frac{\pi}{4}-a\right)-Cos\left(\frac{\pi}{4}-a\right)}\)
Tính giá trị các biểu thức sau:
a) D=\(\frac{9\sin^2x-4\cos^2x}{3\sin^2x+2\cos^2x}\), biết \(\tan x=3\)
b) Cho \(3\sin^4x+\cos^4x=\frac{3}{4}\). Tính A=\(\sin^4x+3\cos^4x\)
chứng minh
a) \(\frac{sin^2a+2cos^2a-1}{cot^2a}=sin^2a\)
b) \(\frac{1-sin^2a.cos^2a}{cos^2a}-cos^2a=tan^2a\)
c) \(\frac{sin^2a-tan^2a}{cos^2a-cot^2a}=tan^6a\)
Chứng minh rằng: Sin(45+a)-cos(45+a)/Sin(45+a)+cos(45+a)=tan a
Chứng minh đẳng thức:
(Sin⁴a-cos⁴a+cos²a)/(2-2cosa)=cos²(a/2)
Chứng minh :
(1-cos x)(1+cos^2 x)=1/1-cos x
(1- cos x).(1+cos^2 x)= 1/1-cosx
