Question

1+cot2 alpha=1/sin^2alpha 

Với góc nhọn alpha  tùy ý. Chứng minh rằng:

 

Answer 1

\(1+cot^2\alpha=1+\left(\dfrac{cos\alpha}{sin\alpha}\right)^2=\dfrac{cos^2\alpha}{sin^2\alpha}+1=\dfrac{cos^2\alpha+sin^2\alpha}{sin^2\alpha}=\dfrac{1}{sin^2\alpha}\)

Answer 2

Ta có: \(1+cot^2\alpha=1+\dfrac{cos^2\alpha}{sin^2\alpha}=\dfrac{sin^2\alpha}{sin^2\alpha}+\dfrac{1-sin^2\alpha}{sin^2\alpha}=\dfrac{sin^2\alpha+1-sin^2\alpha}{sin^2\alpha}=\dfrac{1}{sin^2\alpha}\)