\(\alpha+\beta=90^o\)
Ta có: \(\cos^2\alpha=\sin^2\left(90^o-\alpha\right)=\sin^2\beta\)
\(\cos^2\beta=\sin^2\left(90^o-\beta\right)=\sin^2\alpha\)
\(\Rightarrow\cos^2\alpha-\cos^2\beta=\sin^2\beta-\sin^2\alpha\) (1)
Ta có: \(\tan\alpha=\dfrac{\sin\alpha}{\cos\alpha}\) \(\Rightarrow\sin\alpha=\tan\alpha.\cos\alpha\)
`@` \(\sin^2\alpha+\cos^2\alpha=1\)
`<=>`\(\Rightarrow\tan^2\alpha.\cos^2\alpha+\cos^2\alpha=1\)
`<=>`\(\cos^2\alpha=\dfrac{1}{1+\tan^2\alpha}\)
C/m tương tự, ta có: \(\cos^2\beta=\dfrac{1}{1+\tan^2\beta}\)
`=>` \(\cos^2\alpha-\cos^2\beta=\dfrac{1}{1+\tan^2\alpha}-\dfrac{1}{1+\tan^2\beta}\) (2)
\(\left(1\right);\left(2\right)\Rightarrow\cos^2\alpha-\cos^2\beta=\sin^2\beta-\sin^2\alpha=\dfrac{1}{1+\tan^2\alpha}-\dfrac{1}{1+\tan^2\beta}\)
