5 strategies you can use to solve TRIG IDENTITIES

1. See what you can FACTOR

  • Sometimes, factoring with a common term will make everything into a trig identity
  • ex: tanx ? tanx sin(x) => tanx (1-sin(x)) => tanx cos(x)

2. Multiply the denominator by a CONJUGATE

  • When you see a 1+sinx or a 1+cosx or something like that in a denominator, multiply both the numerator and the denominator by a conjugate (i.e. 1-sinx or 1-cosx)
  • ex: sinx / (1+cosx) => multiply by (1-cosx)/(1-cosx) to make it sinx(1-cosx) / 1-cos(x) => (sinx-sinxcosx) / sin(x)?


  • Whenever you see a fraction added to a non-fraction, try giving them a common denominator
  • ex: sin x + cos x cot x => sin x + cos x (cos x /sin x) => sin(x) / sinx + cos(x) / sinx =>

4. SPLIT UP A FRACTION into two separate fractions

  • When you have multiple terms in the numerator of a fraction, you might want to split them into separate fractions
  • ex: (cscx ? sinx) / cscx => cscx / cscx ? sinx / cscx => 1 ? sin(x) => cos(x)

5. Rewrite everything in terms of SINE AND COSINE

  • Sine and cosine are often the easiest to deal with, so it can help to convert other functions into sine and cosine to make everything simpler
  • secx = 1/cosx
  • tanx = sinx/cosx
  • cscx = 1/sinx
  • cotx = cosx/sinx

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