\(A=\dfrac{1+2sinx.cosx}{cos^2x-sin^2x}=\dfrac{sin^2x+2sinx.cosx+cos^2x}{\left(sinx+cosx\right)\left(cosx-sinx\right)}\)
\(=\dfrac{\left(sinx+cosx\right)^2}{\left(sinx+cosx\right)\left(cosx-sinx\right)}=\dfrac{sinx+cosx}{cosx-sinx}\)
lần sau nhớ ghi góc nha bn :)
Chứng minh các hệ thức:
a) \(\dfrac{cos\text{ α }}{1-sin\text{ α}}=\dfrac{1+sin\text{ α}}{cos\text{ α}}\)
b)\(\dfrac{\left(sin\text{ α }+cos\text{ α }\right)^2-\left(sin\text{ α }-cos\text{ α }\right)^2}{sin\text{ α }cos\text{ α }}=4\)
rút gọn biểu thức :
A = 1 + \(\dfrac{2\sin\alpha.\cos\alpha}{\cos^2\alpha-\sin^2\alpha}\)
B = \(\sin^6\alpha+\cos^6\alpha+3\sin^2\alpha.\cos^2\alpha\)
Rút gọn .
\(A=\dfrac{1+2\sin\alpha\cos\alpha}{\sin\alpha+\cos\alpha}\)
\(B=\left(\sin\alpha+\cos\alpha\right)^2-\left(\cos\alpha-\sin\alpha\right)^2\)
\(C=\dfrac{\left(\sin\alpha-\cos\alpha\right)^2-\left(\sin\alpha+\cos\alpha\right)}{\sin\alpha\cos\alpha}\)
Mấy bạn giúp đỡ được phần nào thì giúp , giúp hết thì tốt quá .
Chứng minh:
a)\(cot^2\alpha-cos^2\alpha\cdot cot^2\alpha=cos^2\alpha\)
b)\(tan^2\alpha-sin^2\alpha\cdot tan^2\alpha=sin^2\alpha\)
c) \(\dfrac{1-cos^2}{sin\alpha}\) = \(\dfrac{sin\alpha}{1+cos\alpha}\)
d)\(tan^2\alpha-sin^2\alpha=tan^2\cdot sin^2\alpha\)
e) \(\sin^6\alpha+cos^6\alpha+3sin^2\cdot cos^2\alpha=1\)
Cho 0o < x < 90o, CM các đẳng thức
1/ \(\dfrac{1}{\tan x+1}+\dfrac{1}{\cot x+1}=1\)
2/ \(\dfrac{\cos x}{\sin x-\cos x}+\dfrac{\sin x}{\sin x+\cos x}=\dfrac{1+\cot^2x}{1-\cot^2x}\)
3/ \(\left(\sqrt{\dfrac{1+\sin x}{1-\sin x}}-\sqrt{\dfrac{1-\sin x}{1+\sin x}}\right)^2=4\tan^2x\)
4/ \(\left(\sqrt{\dfrac{1+\cos x}{1-\cos x}}-\sqrt{\dfrac{1-\cos x}{1+\cos x}}\right)^2=4\cot^2x\)
1)
a) cot2 α+ 1 = \(\dfrac{1}{sin^2a}\)
b)1 + tan2 α = \(\dfrac{1}{cos^2a}\)
c) sin4 α+ cos2α = 2.sin2α . cos2 α
d) \(\dfrac{1-4.sin^2a.cos^2a}{\left(sina+cosa\right)^2}=1-2.sina.cosa\)
e) \(\dfrac{2.sina.cosa-1}{cos^2a-sin^2a}=\dfrac{tana-1}{tana+1}\)
Cho 0o < x < 90o, CM các biểu thức sau không phụ thuộc vào biến:
\(1.A=2\left(\sin^4x+\cos^4x+\sin^2x\cos^2x\right)^2-\left(\sin^8x+\cos^8x\right)\)
\(2.B=\left(\dfrac{1-\tan^2x}{\tan x}\right)^2-\left(1+\tan^2x\right)\left(1+\cot^2x\right)\)
\(3.C=\left(\sin^4x+\cos^4x-1\right)\left(\tan^2x+\cot^2x+2\right)\)
\(4.D=\dfrac{\tan^2x-\cos^2x}{\sin^2x}+\dfrac{\cot^2x-\sin^2x}{\cos^2x}\)
\(5.E=\dfrac{\cot^2x-\cos^2x}{\cot^2x}+\dfrac{\sin x\cdot\cos x}{\cot x}\)
\(A=\dfrac{\sin+4\cos}{2\sin-cos}\)
bt rằng \(\tan=3,Tính:\)
chứng minh 4 = \(\dfrac{\left(sin+cos\right)^2-\left(sin-cos\right)^2}{sin\cdot cos}\)
