CMR

a)\(\frac{1+\cos\alpha}{\sin\alpha}=\frac{\sin\alpha}{1-\cos\alpha}\)

b)\(\frac{\tan\alpha+1}{\tan\alpha-1}=\frac{1+\cot\alpha}{1-\cot\alpha}\)

c) \(\tan^2\alpha-\sin^2\alpha=\tan^2\alpha.\sin^2\alpha\)

d)\(\frac{1-4\sin^2\alpha.\cos^2\alpha}{\left(\sin\alpha-\cos\alpha\right)^2}=\left(\sin\alpha+\cos\alpha\right)^2\)

CMR: \(\frac{\sin^2\alpha}{\cos\alpha\left(1+\tan\alpha\right)}-\frac{\cos^2\alpha}{\sin\alpha\left(1+\cot\alpha\right)}=\sin\alpha-\cos\alpha\)

Tính: 

\(C=\frac{\tan^2\alpha\left(1+\cos^3\alpha\right)+\cot^2\alpha\left(1+\sin^3\alpha\right)}{\left(\sin^3\alpha+\cos^3\alpha\right)\left(1+\sin^3\alpha+\cos\alpha\right)}\)

Biết \(\tan\alpha=\tan35^o.\tan36^o.\tan37^o.....\tan57^o\)

Cho \(\sin\alpha+\cos\alpha=\frac{\sqrt{6}}{2},a\in\left(0;\frac{\pi}{4}\right)\)

Tính giá trị biểu thức: \(P=\cos\left(\alpha+\frac{\pi}{4}\right)+\sqrt{2\left(1-\sin\alpha\cos\alpha+\sin\alpha-\cos\alpha\right)}\)

Cho góc nhọn \(\alpha\)thỏa mãn \(\tan\alpha=\frac{2}{\sqrt{3}}\). Tính: \(B=\frac{\cos^4\alpha+\sin^2\alpha\left(\cos^2\alpha+1\right)}{2\cos^4\alpha+2\sin^2\cos^2-\frac{3}{5}\sin^2\alpha}\)

1. \(cos^225-\sin23+\cos67-\frac{3\tan54}{\cot36}+\cos^265\)
2. \(\sin^4\alpha+\cos^4\alpha+2\sin\alpha.\cos\alpha\)
3. \(tan^2\alpha\left(2cos^2\alpha+sin^2\alpha-1\right)\)
4. \(\left(\tan\alpha+\cot\alpha\right)^2-\left(\tan\alpha-\cot\alpha\right)^2\)