trig identities trig identities cheat sheet

Show that cos4(x) - sin4(x) = cos(2x) STEP 1: Everything is already in sin and cos, so this part is done. STEP 7: Now, both sides should be exactly equal, or obviously equal, and you have proven your identity. STEP 6: Factor numerators and denominators, then cancel any common factors. STEP 5: Replace cos powers greater than 2 with sin powers using the Pythagorean identities. STEP 4: Expand any equations you can, combine like terms, and simplify the equations. STEP 3: Check for angle multiples and remove them using the appropriate formulas. STEP 2: Check all the angles for sums and differences and use the appropriate identities to remove them. Most of this can be done using the quotient and reciprocal identities. STEP 1: Convert all sec, csc, cot, and tan to sin and cos. As you gain more practice, you can skip or combine these steps when you recognize other identities. It is rather tedious, and can take more time than necessary. The following seven step process will work every time.

Solving trig identities takes practice! Quotient Identities: tan(x) = sin(x)/cos(x) cot(x) = cos(x)/sin(x) Reciprocal Identities: csc(x) = 1/sin(x) sec(x) = 1/cos(x) cot(x) = 1/tan(x) sin(x) = 1/csc(x) cos(x) = 1/sec(x) tan(x) = 1/cot(x) Pythagorean Identities: sin2(x) + cos2(x) = 1 cot2A +1 = csc2A 1+tan2A = sec2A (For a list of other important identities, see the Trig Cheat Sheet article in this series.) How to Solve Trig Identities The following identities are essential to all your work with trig functions. The more basic formulas you have memorized, the faster you will be. The trick to solve trig identities is intuition, which can only be gained through experience.

Trig identities trig identities cheat sheet