\(sin^2\alpha+cos^2\alpha=1\Rightarrow cos\alpha=\sqrt{1-sin^2\alpha}=\sqrt{1-\left(\frac{7}{25}\right)^2}=\frac{24}{25}\)
\(tan\alpha=\frac{sin\alpha}{cos\alpha}=\frac{\frac{7}{25}}{\frac{24}{25}}=\frac{7}{24}\)
\(cot\alpha=\frac{1}{tan\alpha}=\frac{1}{\frac{7}{24}}=\frac{24}{7}\)
CMR: \(\frac{\sin^2\alpha}{\cos\alpha\left(1+\tan\alpha\right)}-\frac{\cos^2\alpha}{\sin\alpha\left(1+\cot\alpha\right)}=\sin\alpha-\cos\alpha\)
a) Biết \(\sin\alpha=\frac{2}{5}\) hãy tính \(\cos\alpha,\tan\alpha,\cot\alpha\)
b) Biết \(\tan\alpha=\frac{12}{35}\)hãy tính \(\sin\alpha,\cos\alpha,\cot\alpha\)
Tinh ti so luong giac sau :
\(\sin\alpha\times\cos\alpha+\frac{\sin^2\alpha}{1+\cot\alpha}+\frac{\cos^2\alpha}{1+\tan\alpha}\)
Chứng minh:
\(a,tan\alpha=\frac{sin\alpha}{cos\alpha}\)
\(b,cot\alpha=\frac{cos\alpha}{sin\alpha}\)
Rút gọn các biểu thức:
a)\(\left(\sin\alpha+\cos\alpha\right)^2+\left(\sin\alpha-\cos\alpha\right)^2\)
b)\(\cot^2\alpha-\cos^2\alpha.\cot^2\alpha\)
c)\(\sin\alpha.\cos\alpha\left(\tan\alpha+\cot\alpha\right)\)
d)\(\tan^2\alpha-\sin^2\alpha.\tan^2\alpha\)
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/ \(\cot^2\alpha-\cos^2\alpha=\cot^2\alpha.\cos\alpha\)
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: \(\tan\alpha.\cot\alpha=1\Rightarrow\cot\alpha=\frac{\sqrt{5}}{2}\)
Câu 50**: Cho góc nhọn 
tuỳ ý giá trị biểu thức \(\dfrac{tan\alpha}{cot\alpha}+\dfrac{cot\alpha}{tan\alpha}-\dfrac{sin^2\alpha}{cos^2\alpha}\) bằng
A. \(tan^2\alpha\) ; B . \(cot^2\alpha\) ; C . 0 ; D. 1 .
