Question

Cos2 0-cos 20 = sin2 0

Answer 1

`\begin{gathered} \cos ^2(x)-\cos (2x)=sen^2(x) \\ \text{ }\cos ^2(x)-sen^2(x)\text{ = }\cos (2x) \\ \end{gathered}`

According to Double identities

`\cos (2x)=2cos^2(x)-1`
`\begin{gathered} \cos ^2(x)-sen^2(x)=2\cos ^2(x)-1 \\ -sen^2(x)=2\cos ^2(x)-\cos ^2(x)-1 \\ -sen^2(x)=\cos ^2(x)-1 \\ 1=\cos ^2(x)+sen^2(x) \end{gathered}`