Wie beweisen Sie cosX / (secX - tanX) = 1 + sinX ?
Antworten:
Wie nachstehend.
Erläuterung:
Beweisen cos x / (sec x - tan x) = (1 + sin x)
LHS = cos x / ((1/cos x) - (sin x / cos x) as color(blue)(sec x = 1/cos x, tan x = sin x / cos x
=> cos x / ((1 - sin x) / cos x) as color(green)(cos x ist das LCM des Nenners.
=> cos^2 x / (1 - sin x)
=> = (1 - sin^2 x) / (1 - sin x) as color(blue)(cos^2x = 1 - sin^2x
=> ((1+ sin x) *color(red)(cancel (1 - sin x))) /color(red)(cancel (1 - sin x))
=> 1 + sin x
QED