Wie vereinfacht man (sec ^ 2x) - (tan ^ 2x) ?

Antworten:

sec^2 x - tan^2 x = 1

Erläuterung:

Beachten Sie, dass:

sin^2 x + cos^2 x = 1

Daher:

cos^2 x = 1 - sin^2 x

und wir finden:

sec^2 x - tan^2 x = 1/cos^2 x - sin^2 x/cos^2 x

color(white)(sec^2 x - tan^2 x) = (1 - sin^2 x)/cos^2 x

color(white)(sec^2 x - tan^2 x) = cos^2 x/cos^2 x

color(white)(sec^2 x - tan^2 x) = 1