\(1+\tan^2a=1+\frac{\sin^2a}{\cos^2a}=\frac{\sin^2a+\cos^2a}{\cos^2a}=\frac{1}{\cos^2a}\)
\(1+\cot^2a=1+\frac{\cos^2a}{\sin^2a}=\frac{\sin^2a+\cos^2a}{\sin^2a}=\frac{1}{\sin^2a}\)
CMR\(\frac{1-2\cos^2\alpha}{1+2\sin\alpha.\cos\alpha}=\frac{\sin\alpha-\cos\alpha}{\sin\alpha+\cos\alpha}\)
Chứng minh các hệ thức sau:
a) \(\frac{1-cos\alpha}{sin\alpha}=\frac{sin\alpha}{1+cos\alpha}\)
b) \(tan^2\alpha-sin^2\alpha=tan^2\alpha.sin^2\alpha\)
c) \(\frac{1-tan\alpha}{1+tan\alpha}=\frac{cos\alpha-sin\alpha}{cos\alpha+sin\alpha}\)
1. Chứng minh rằng: \(\frac{1-2\sin.\cos\alpha}{sin^2\alpha-\cos^2\alpha}=\frac{sin\alpha-\cos\alpha}{sin\alpha+\cos\alpha}\) (\(\alpha\ne45^o\))
2. Chứng minh: \(\cos^4\alpha+\sin^2\alpha.\cos^2\alpha+\sin^2\alpha\) không phụ thuộc vào x
Chứng minh:
a)\(\cos^4\alpha-sin^4\alpha=2cos^2\alpha-1\)
b)\(\frac{cos\alpha}{1-sin\alpha}=\frac{1+sin\alpha}{cos\alpha}\)
c)\(\frac{\left(sin\alpha+cos\alpha\right)^2-\left(sin\alpha-cos\alpha\right)^2}{sin\alpha.cos\alpha}=4\)
Mình cần gấp!!!
CMR: \(\frac{\sin^2\alpha}{\cos\alpha\left(1+\tan\alpha\right)}-\frac{\cos^2\alpha}{\sin\alpha\left(1+\cot\alpha\right)}=\sin\alpha-\cos\alpha\)
\(\left(1+\tan^2\alpha\right)\cos^2\alpha+\left(1+\cot^2\alpha\right)\sin^2\alpha\)
\(=\left(1+\frac{\sin^2\alpha}{\cos^2\alpha}\right)\cos^2\alpha+\left(1+\frac{\cos^2\alpha}{\sin^2\alpha}\right)\sin^2\alpha\)
\(=\cos^2\alpha+\sin^2\alpha+\sin^2\alpha+\cos^2\alpha\)
\(=2\sin^2\alpha+2\cos^2\alpha\)
đúng hay sai zậy các bạn
Ta có: \(\sin^2\alpha+\cos^2\alpha=1\). lại có : \(\sin\alpha=\frac{2}{3}\)
=> \(\frac{4}{9}+\cos^2\alpha=1\)
=> \(\cos^2\alpha=\frac{5}{9}\Rightarrow\cos\alpha=\frac{\sqrt{5}}{3}\)
Mà \(\tan\alpha=\frac{\sin\alpha}{\cos\alpha}=\frac{2}{3}:\frac{\sqrt{5}}{3}=\frac{2}{\sqrt{5}}\)
mặt khác: \(\tan\alpha.\cot\alpha=1\Rightarrow\cot\alpha=\frac{\sqrt{5}}{2}\)
Tinh ti so luong giac sau :
\(\sin\alpha\times\cos\alpha+\frac{\sin^2\alpha}{1+\cot\alpha}+\frac{\cos^2\alpha}{1+\tan\alpha}\)
1) Cho: \(\tan\alpha=\frac{1}{2}\). Tính \(\frac{\cos\alpha+\sin\alpha}{\cos\alpha-\sin\alpha}\)
2) Cho: \(\cos\beta=2\sin\beta.\) Hãy tính: \(\sin\beta.\cos\beta\)
3)Chứng minh hệ thức:
a/ \(\frac{1+\cos\alpha}{\sin\alpha}=\frac{\sin\alpha}{1-\cos\alpha}\)
b/ \(\cot^2\alpha-\cos^2\alpha=\cot^2\alpha.\cos\alpha\)
