RECIPROCAL IDENTITIES
sin α csc α = 1
cos α sec α = 1
tan α cot α = 1
PYTHAGORAS IDENTITIES
sin2
α + cos2 α = 1
sec2
α + tan2 α = 1
csc2
α + cot2 α = 1
RATIO IDENTITIES
EUIVALENT FORM OF THE BASIC IDENTITIES
sin α csc α = 1
cos α sec α = 1
tan α cot α = 1
sin2
α +
cos2 α = 1
1 +
tan2 α = sec2 α
1 +
cot2 α = csc2 α
cos α tan α = sin α
sin α cot α = cos α
sin2
α = 1 – cos2 α
1 + tan2 α = sec2
α
1 + cot2
α = csc2
α
cos2
α = 1
– sin2 α
tan2
α = sec2
α - 1
cot2
α = csc2
α - 1
SUM AND DIFERENCE OF TWO ARGUMENT
cos (α + β) + cos (α –
β) =
2 cos α cos β
cos (α + β) - cos (α
– β) = - 2 sin α
sin β
sin (α + β) + sin (α
– β) =
2 sin α cos β
sin (α + β) - sin (α
– β) =
2 cos α sin β
PRODUCT
sin α cos β = ½ [ sin (α+β) + sin
(α-β) ]
sin α sin β = - ½ [ cos (α+β) - cos
(α-β) ]
cos α sin β = ½ [ sin (α+β) - sin
(α-β) ]
cos α cos β = ½ [ cos (α+β) + cos (α-β) ]
HALF ARGUMENT
DOUBLE
ARGUMENT
sin 2α = sin (α+α)
= sin α
cos α + cos α
sin α
= sin α cos α
+ sin α cos α
= 2 sin α cos α
cos 2α = cos (α+α)
= cos α cos α - sin
α sin α
= ( cos α)2 – (sin α)2
= cos2 α – sin2 α
= ( 1 - sin2 α) – sin2 α
= 1 – 2 sin2 α
atau
cos 2α = cos (α+α)
= cos α cos α - sin
α sin α
= ( cos α)2 – (sin α)2
= cos2 α – sin2 α
= cos2 α – ( 1
- cos2 α )
= 2 cos2 α – 1
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