Method of proving trignometric identities

2,090

In general, there is no one universal method for all problems. But there are some guidelines:

$1$: Look at the problem and see if some known trigonometric identities can help. For instance, can we use $\sin^2(x) + \cos^2(x) = 1$ somewhere to simplify?

$2$: Make use of some algebraic identities: For instance, $\sin^2(x) - \cos^2(x) = (\sin(x) - \cos(x))(\sin(x) + \cos(x))$, which stems from the fact that $a^2-b^2 = (a+b)(a-b)$.

$3$: Look at what you want to prove and simplify accordingly. For instance, if the right hand side is just in terms of $\sin(x)$ and $\cos(x)$, then expressing all the trigonometric functions on the left hand side as function of $\sin(x)$ and $\cos(x)$ might be helpful.

The list goes on and on. At the end of the day, you need to pick the right tool to attack the problem. So make sure to possess lot of useful mathematical tools.

Share:
2,090

Related videos on Youtube

user3034084
Author by

user3034084

Updated on August 01, 2022

Comments

  • user3034084
    user3034084 over 1 year

    How do we prove trigonometric identities?

    When my teacher did it in school today all I could see was him doing random steps. I didn't really understand his method. I am basically asking whether my process is correct or not. If not what is wrong and how to improve it. I need someone to me the steps of solving trigonometric identities/ trigonometry method.

    From what I have understood:

    1. Check expression to see if you can simplify e.g. cancel out

    2. Check expression to see if their are any trig identities you can sub in

    3. Simply by cancelling out or by using foil or by factoring

    4. Check expression to see if their are any trig identities you can sub in?

    5. Simply by cancelling out or by using foil or by factoring