Wie verifizierst du `cos ^ 2 (x) -sin ^ 2 (x) = 1-2sin ^ 2 (x)`?

RTP: `cos^2x-sin^2x=1-2sin^2x`

LHS:
`cos^2x-sin^2x`

Erinnern: `cos^2x+sin^2x=1` so `cos^2x=1-sin^2x`

= `(1-sin^2x)-sin^2x`

=`1-sin^2x-sin^2x`

= `1-2sin^2x`

= RHS

Deshalb: `cos^2x-sin^2x=1-2sin^2x`