Dezember 24, 2019

von Rica

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

Antworten:

${sec}^{2} x - {tan}^{2} x = 1$ $sec^2 x - tan^2 x = 1$

Erläuterung:

Beachten Sie, dass:

${sin}^{2} x + {cos}^{2} x = 1$ $sin^2 x + cos^2 x = 1$

Daher:

${cos}^{2} x = 1 - {sin}^{2} x$ $cos^2 x = 1 - sin^2 x$

und wir finden:

${sec}^{2} x - {tan}^{2} x = \frac{1}{{cos}^{2} x} - \frac{{sin}^{2} x}{{cos}^{2} x}$ $sec^2 x - tan^2 x = 1/cos^2 x - sin^2 x/cos^2 x$

${sec}^{2} x - {tan}^{2} x = \frac{1 - {sin}^{2} x}{{cos}^{2} x}$ $color(white)(sec^2 x - tan^2 x) = (1 - sin^2 x)/cos^2 x$

${sec}^{2} x - {tan}^{2} x = \frac{{cos}^{2} x}{{cos}^{2} x}$ $color(white)(sec^2 x - tan^2 x) = cos^2 x/cos^2 x$

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