Verifying Trig Identities

When verifying trigonometric identities, you should first work with the toughest side of the equation. Do not move things from one side of the equation to the other. You need to look for things that factor while simplifying the equation by adding the fractions if there are any. If you see a place to substitute using another trig identity, use it to get the trig functions that go together well like sine and cosine, or secant and tangent. Sometimes the best strategy is to get everything into terms of sines and cosines if you get stuck. Both sides of the equation should look exactly the same when you are done with the problem.

Sum and Difference Formulas

Sum and difference formulas are used to find exact values of trigonometric functions that use sums or differences of the special angles to get different angles.
Ex: Cos75° = Cos(30° + 45°)

sin(A+B) = (sinAcosB) + (cosAsinB)                                                cos(A+B) = (cosAcosB) - (sinAsinB)
sin(A-B) = (sinAcosB) - (cosAsinB)                                                 cos(A-B) = (cosAcosB)+ (sinAsinB)
tan(A+B) = (tanA + tanB) / (1 - tanAtanB)                                       tan(A-B) = (tanA - tanB) / (1 + tanAtanB)

Double Angle Formulas

sin2A = 2sinAcosA                                                                           tan2A = (2tanA) / (1 - tan²A)
cos2A = cos²A -sin²A = 2cos²A - 1 = 1 - 2sin²A                            

Half Angle Formulas


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