Advanced Precalculus             Chapter 7 Formula Sheet 
                      
                      
                     Sum and Difference Formulas:                             Double-Angle Formulas: 
                      
                         (     )
                     cos α +β = cosαcosβ−sinαsinβ                              sin2θ = 2sinθcosθ 
                         (     )                                                           2       2
                     cos α −β = cosαcosβ+sinαsinβ                              cos2θ = cos θ−sin θ 
                        (     )                                                              2
                     sin α + β = sinαcosβ+cosαsinβ                             cos2θ = 2cos θ−1 
                        (     )                                                                2
                     sin α −β = sinαcosβ−cosαsinβ                              cos2θ =1−2sin θ 
                         (    )   tanα+tanβ                                       ( )     2tanθ
                     tan α +β = 1−tanαtanβ                                     tan 2θ = 1− tan2 θ  
                         (    )   tanα−tanβ
                     tan α −β = 1+ tanαtanβ  
                      
                     Power Reducing Formulas:                                 Half-Angle Formulas: 
                      
                     sin2 θ = 1−cos2θ                                          sin α = ± 1−cosα  
                                  2                                               2          2
                      
                     cos2 θ = 1+cos2θ                                          cosα = ± 1+cosα  
                                   2                                               2          2
                      
                     tan2 θ = 1−cos2θ                                 tan α = ± 1−cosα = 1−cosα =          sinα    
                              1+cos2θ                                     2      1+cosα        sinα      1+cosα
                      
                     Product-to-Sum Formulas:                                 Sum-to-Product Formulas: 
                      
                                  1    (     )      (    )                                        α+β      α−β
                                   [                      ]
                     sinαsinβ = 2 cos α −β −cos α +β                           sinα + sinβ = 2sin   2 cos 2  
                                   1     (    )      (     )                                      α−β      α+β
                                     [                     ]
                     cosαcosβ = 2 cos α−β +cos α+β                             sinα −sinβ = 2sin   2 cos 2  
                                  1    (     )     (     )                                          α+β      α−β
                                    [                    ]
                     sinαcosβ = 2 sin α +β +sin α −β                           cosα+cosβ=2cos 2 cos 2  
                                                                               cosα−cosβ= −2sinα+βsinα−β  
                                                                                                      2        2