Forumet - Matematik D, trigonometri fråga!

Matematik D, trigonometri fråga!

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elcopo:

visa att:


elcopo:

tan2x=2tanx/(1-tan^2x)


sin² x+cos² x = 1

sin(x+y) = sin x cos y+cos x sin y
cos(x+y) = cos x cos y-sin x sin y

sin 2x = sin(x+x)
sin 2x = sin x cos x+cos x sin x
sin 2x = sin x cos x+sin x cos x
sin 2x = 2 sin x cos x

cos 2x = cos(x+x)
cos 2x = cos x cos x-sin x sin x
cos 2x = cos² x-sin² x
cos 2x = cos² x-sin² x+sin² x-sin² x
cos 2x = sin² x+cos² x-sin² x-sin² x
cos 2x = (sin² x+cos² x)-(sin² x+sin² x)
cos 2x = 1-2 sin² x
cos 2x = cos² x-sin² x+cos² x-cos² x
cos 2x = cos² x+cos² x-sin² x-cos² x
cos 2x = (cos² x+cos² x)-(sin² x+cos² x)
cos 2x = 2 cos² x-1
cos 2x = cos² x-sin² x = 1-2 sin² x = 2 cos² x-1

tan 2x = sin 2x/cos 2x
tan 2x = 2 sin x cos x/(cos² x-sin² x)
tan 2x = (2 sin x cos x/(cos² x-sin² x))/(cos² x/cos² x)
tan 2x = (2 sin x cos x/cos² x)/((cos² x-sin² x)/cos² x)
tan 2x = (2 sin x/cos x)/(1-sin² x/cos² x)
tan 2x = (2 sin x/cos x)/(1-(sin x/cos x)²)
tan 2x = 2 tan x/(1-tan² x)

[

tan(x+y) = sin(x+y)/cos(x+y)
tan(x+y) = (sin x cos y+cos x sin y)/(cos x cos y-sin x sin y)
tan(x+y) = ((sin x cos y+cos x sin y)/(cos x cos y-sin x sin y))/(cos x cos y/(cos x cos y))
tan(x+y) = ((sin x cos y+cos x sin y)/(cos x cos y))/((cos x cos y-sin x sin y)/(cos x cos y))
tan(x+y) = (sin x cos y/(cos x cos y)+cos x sin y/(cos x cos y))/(cos x cos y/(cos x cos y)-sin x sin y/(cos x cos y))
tan(x+y) = (sin x/cos x+sin y/cos y)/(1-sin x sin y/(cos x cos y))
tan(x+y) = (sin x/cos x+sin y/cos y)/(1-(sin x/cos x)sin y/cos y)
tan(x+y) = (tan x+tan y)/(1-tan x tan y)

tan 2x = tan(x+x)
tan 2x = (tan x+tan x)/(1-tan x tan x)
tan 2x = 2 tan x/(1-tan² x)

]