Question

CM:\(a.sin^2\alpha+cos^2\alpha=1\\ b.cot^2\alpha.cos^2\alpha=cot^2\alpha-cos^2\alpha\)

Answer 1

a) ta có : \(VT=sin^2\alpha+cos^2\alpha=\left(\dfrac{đối}{huyền}\right)^2+\left(\dfrac{kề}{huyền}\right)^2\)

\(=\dfrac{\left(đối\right)^2+\left(kề\right)^2}{\left(huyền\right)^2}=\dfrac{\left(huyền\right)^2}{\left(huyền\right)^2}=1=VP\left(đpcm\right)\)

b) ta có : \(VP=cot^2\alpha-cos^2\alpha=\dfrac{cos^2\alpha}{sin^2\alpha}-cos^2\alpha=cos^2\alpha\left(\dfrac{1}{sin^2\alpha}-1\right)\)

\(=cos^2\alpha\left(\dfrac{1-sin^2\alpha}{sin^2\alpha}\right)=cos^2\alpha\dfrac{cos^2\alpha}{sin^2\alpha}=cos^2\alpha.cot^2\alpha=VT\left(đpcm\right)\)