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ss_6_2

# ss_6_2 - Section 6.2 Sum and Dierence Formulas This section...

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Section 6.2 Sum and Difference Formulas This section contains important trigonometric identities for finding the trigonometric functions of the sums and differences of angles. cos( α + β ) = cos α cos β - sin α sin β cos( α - β ) = cos α cos β + sin α sin β Example. cos 15 o = cos(60 o - 45 o ) = cos 60 o cos 45 o + sin 60 o sin 45 o = ( 1 2 )( 2 2 ) + ( 3 2 )( 2 2 ) = 2 4 + 6 4 = 1 4 ( 2 + 6) Example. cos( 7 π 12 ) = cos( π 3 + π 4 ) = cos π 3 cos π 4 - sin π 3 sin π 4 = ( 1 2 )( 2 2 ) - ( 3 2 )( 2 2 ) = 2 4 - 6 4 = 1 4 ( 2 - 6) sin( α + β ) = sin α cos β + cos α sin β sin( α - β ) = sin α cos β - cos α sin β Example. sin 15 o = sin(45 o - 30 o ) = sin 45 o cos 30 o - cos 45 o sin 30 o = 2 2 3 2 - 2 2 1 2 = 6 4 - 2 4 = 1 4 ( 6 - 2) cos( π 2 - θ ) = sin θ all θ sin( π 2 - θ ) = cos θ all θ Validation of above: cos( π 2 - θ ) = cos π 2 cos θ + sin π 2 sin θ = (0) cos θ + (1) sin θ = sin θ tan( α + β ) = tan α +tan β 1 - tan α tan β tan( α - β ) = tan α - tan β 1+tan α tan β Proof of the above: tan( α + β ) = sin( α + β ) cos( α + β ) = sin

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