5 strategies you can use to solve TRIG IDENTITIES

Ernest Wolfe

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Feb 23, 2017 · 1 min read

• 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