CMR: Với mọi góc nhọn \(\alpha\) ta có :

\(a,\sin^2\alpha+\cos^2\alpha=1\)

\(b,\tan\alpha=\frac{\sin\alpha}{\cos\alpha}\)

\(c,\tan^2\alpha+1=\frac{1}{\cos^2\alpha}\)

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

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. a) CMR : A =\(\frac{1-2\sin\alpha.\cos\alpha}{sin^2\alpha-cos^2\alpha}=\frac{\sin\alpha-\cos\alpha}{\sin\alpha+\cos\alpha}\)

b) Tính A khi \(\tan\alpha\) =\(\frac{1}{3}\)

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

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

CM các hệ thức sau:

a) \(1+\tan^2\alpha=\frac{1}{\cos^2\alpha}\)
b) \(1+\cot^2\alpha=\frac{1}{\sin^2\alpha}\)
c) \(\cot^2\alpha-\cos^2\alpha=\cot^2\alpha.\cos^2\alpha\)
d) \(\frac{1+\cos\alpha}{\sin\alpha}=\frac{\sin\alpha}{1-\cos\alpha}\)