Tips and tricks for Trigonometric identities
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The trick to proving trig identities is intuition, which can only be gained through experience. The more basic formulas you have memorized, the faster you will be. The following identities are essential to all your work with trig functions. Make a point of memorizing them.Quotient Identities:
How to Solve Them Correctly Every TimeThe following seven step process will work every time. It is rather tedious, and can take more time than necessary. As you gain more practice, you can skip or combine these steps when you recognize other identities.
STEP 1: Convert all sec, csc, cot, and tan to sin and cos. Most of this can be done using the quotient and reciprocal identities.
STEP 2: Check all the angles for sums and differences and use the appropriate identities to remove them.
STEP 3: Check for angle multiples and remove them using the appropriate formulas.
STEP 4: Expand any equations you can, combine like terms, and simplify the equations.
STEP 5: Replace cos powers greater than 2 with sin powers using the Pythagorean identities.
STEP 6: Factor numerators and denominators, then cancel any common factors.
STEP 7: Now, both sides should be exactly equal, or obviously equal, and you have proven your identity.
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