5 strategies you can use to solve TRIG IDENTITIES
1. See what you can FACTOR
Published in
1 min readFeb 23, 2017
- Sometimes, factoring with a common term will make everything into a trig identity
- ex: tanx — tanx sin²(x) => tanx (1-sin²(x)) => tanx cos²(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-cos²(x) => (sinx-sinxcosx) / sin²(x)…
3. Get a COMMON DENOMINATOR
- 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) => sin²(x) / sinx + cos²(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 — sin²(x) => cos²(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
