PROVING IDENTITIES
Proving identities can be fun with a few easy tricks and tips.
Tips & Strategies
- A proof is just filling what lies between the beginning and the end, don't get overwhelmed!
- Start with the more complicated side, you are usually trying to make a complicated expression simple
- If you don't know how to go on, convert the whole expression to sines and cosines
- Always remember the end result you are working for & only make moves that will bring you closer to the finish line
- Combine any fractions by using common denominators
REMEMBER!
Proving identities is not like solving normal math equations. Instead, it is a lot of trial and error. You won't always be able to solve it your first try. Just take your time.
Proving identites doesn't have to be hard.
When proving identities it's important to remember the following identites and always keep them in mind. They can be very helpful for solving the trickier identities.
When proving identities it's important to remember the following identites and always keep them in mind. They can be very helpful for solving the trickier identities.
Example 2tan(x) + cot(x) = sec(x)csc(x)
= sin(x)/cos(x) + cos(x)/sin(x) = (sin(x)/cos(x) * sin(x)/sin(x)) + (cos(x)/sin(x) * cos(x)/cos(x) = (sin2(x) + cos2(x))/sin(x)cos(x) = 1/sin(x)cos(x) = 1/sin(x) * 1/cos(x) = sec(x)csc(x) |
Given
Basic Identity Common Denominator Simplify Pythagorean Identity Break Fraction Basic Identity |
TIP: If you are stuck, work from both sides
EXTRA CHALLENGE PROBLEMS
**Now Try Solving Identities**
cot(x) = cos(x) / sin(x)
Multiply each side by sin(x).
Subtract cos(x) from each side.
Factor out cos(x).
cos^2(x) - 1 = -sin^2(x)
Solve.