Tożsamości trygonometryczne

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Question		Answer
sin" α + cos" α= start learning		1
sin α = #cos α# start learning		+/- \\|1 - cos" α\
cos α = #sin α# start learning		+/- \\|1 - sin" α\
tg α= #sin & cos# start learning		sin α/ cos α
ctg α = #sin & cos# start learning		cos α / sin α
tg α * ctg α = start learning		1
sin" α = (cos) start learning		1 - cos" α
cos" α= (sin) start learning		1 - sin" α
sin(α+β)= start learning		sin αcos β + sin βcos α
sin(α-β)= start learning		sin αcos β - sin βcos α
cos(α+β)= start learning		cos αcos β - sin αsin β
cos(α-β)= start learning		cos αcos β + sin αsin β
cos 2α = start learning		cos²α - sin²α = 2cos²α -1 = 1 -2sin²α = (1 -tg² α)/(1 +tg² α)
sin 2α= start learning		2sin α*cos α = (2tg α)/(1 +tg² α)
sin α + sin β= start learning		2* sin([α+β]/2) * cos([α-β]/2)
sin α - sin β= start learning		2* sin([α-β]/2) * cos([α+β]/2)
cos α + cos β= start learning		2* cos([α+β]/2) * cos([α-β]/2)
cos α - cos β= start learning		-2* sin([α+β]/2) * sin([α-β]/2)
tg (α+β)= start learning		(tg α +tg β)/(1 -tg α*tg β)
tg(α -β)= start learning		(tg α -tg β)/(1 +tg α*tg β)
tg 2α= start learning		(2tg α)/(1 -tg² α)
sin α= #x, y, r# start learning		y / r
cos α= #x, y, r# start learning		x / r
tg α= #x, y, r# start learning		y / x
ctg α= #x, y, r# start learning		x / y
sin α sin β= start learning		-0.5(cos(α+β)-cos(α-β))
cos α cos β= start learning		0.5(cos(α+β)+cos(α-β))
sin α cos β= start learning		0.5(sin(α+β)+sin(α-β))

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