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identities

# identities - sin α 2 = ± r 1-cos α 2 cos α 2 = ± r 1...

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Trigonometric Identities Fundamental Identities Reciprocal Identities sin x = 1 csc x cos x = 1 sec x tan x = 1 cot x csc x = 1 sin x sec x = 1 cos x cot x = 1 tan x Quotient Identities tan x = sin x cos x cot x = cos x sin x Pythagorean Identities sin 2 x + cos 2 x = 1 1 + tan 2 x = sec 2 x 1 + cot 2 x = csc 2 x Even-Odd Identities sin( - x ) = - sin x cos( - x ) = cos x tan( - x ) = - tan x csc( - x ) = - csc x sec( - x ) = sec x cot( - x ) = - cot x Sum and Difference Formulas cos( α + β ) = cos α cos β - sin α sin β cos( α - β ) = cos α cos β + sin α sin β sin( α + β ) = sin α cos β + cos α sin β sin( α - β ) = sin α cos β - cos α sin β tan( α + β ) = tan α + tan β 1 - tan α tan β tan( α - β ) = tan α - tan β 1 + tan α tan β Double-Angle Formulas sin 2 θ = 2 sin θ cos θ cos 2 θ = cos 2 θ - sin 2 θ = 2 cos 2 θ - 1 = 1 - 2 sin 2 θ tan 2 θ = 2 tan θ 1 - tan 2 θ Power-Reducing Formulas sin 2 θ = 1 - cos 2 θ 2 cos 2 θ = 1 + cos 2 θ 2 tan 2 θ = 1 - cos 2 θ 1 + cos 2 θ

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Half-Angle Formulas
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Unformatted text preview: sin α 2 = ± r 1-cos α 2 cos α 2 = ± r 1 + cos α 2 tan α 2 = ± r 1-cos α 1 + cos α = 1-cos α sin α = sin α 1 + cos α Product to Sum Formulas sin A cos B = 1 2 [sin( A + B ) + sin( A-B )] cos A sin B = 1 2 [sin( A + B )-sin( A-B )] cos A cos B = 1 2 [cos( A + B ) + cos( A-B )] sin A sin B = 1 2 [cos( A-B )-cos( A + B )] Sum to Product Formulas sin α + sin β = 2 sin α + β 2 cos α-β 2 sin α-sin β = 2 cos α + β 2 sin α-β 2 cos α + cos β = 2 cos α + β 2 cos α-β 2 cos α-cos β =-2 sin α + β 2 sin α-β 2...
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identities - sin α 2 = ± r 1-cos α 2 cos α 2 = ± r 1...

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