Chứng minh đẳng thức sau Cota – Tana = 2cot2a 28/08/2021 Bởi Anna Chứng minh đẳng thức sau Cota – Tana = 2cot2a
`cotalpha-tanalpha=cosalpha/sinalpha-sinalpha/cosalpha={cos^2alpha-sin^2alpha}/{sinalpha.cosalpha}={cos2alpha}/{sinalpha.cosalpha}={2cos2alpha}/{sin2alpha}=2cot2alpha` (ĐPCM) Bình luận
Ta có:$\cot \left(α\right)-\tan \left(α\right)=\frac{\cos \left(α\right)}{\sin \left(α\right)}-\tan \left(α\right)=\frac{\cos \left(α\right)}{\sin \left(α\right)}-\frac{\sin \left(α\right)}{\cos \left(α\right)}=\frac{\cos ^2\left(α\right)}{\sin \left(α\right)\cos \left(α\right)}-\frac{\sin ^2\left(α\right)}{\sin \left(α\right)\cos \left(α\right)}=\frac{\cos ^2\left(α\right)-\sin ^2\left(α\right)}{\sin \left(α\right)\cos \left(α\right)}=2\cot \left(2α\right)$ (đpcm) Xin hay nhất :d Bình luận
`cotalpha-tanalpha=cosalpha/sinalpha-sinalpha/cosalpha={cos^2alpha-sin^2alpha}/{sinalpha.cosalpha}={cos2alpha}/{sinalpha.cosalpha}={2cos2alpha}/{sin2alpha}=2cot2alpha` (ĐPCM)
Ta có:$\cot \left(α\right)-\tan \left(α\right)=\frac{\cos \left(α\right)}{\sin \left(α\right)}-\tan \left(α\right)=\frac{\cos \left(α\right)}{\sin \left(α\right)}-\frac{\sin \left(α\right)}{\cos \left(α\right)}=\frac{\cos ^2\left(α\right)}{\sin \left(α\right)\cos \left(α\right)}-\frac{\sin ^2\left(α\right)}{\sin \left(α\right)\cos \left(α\right)}=\frac{\cos ^2\left(α\right)-\sin ^2\left(α\right)}{\sin \left(α\right)\cos \left(α\right)}=2\cot \left(2α\right)$ (đpcm)
Xin hay nhất :d