How would you show that one trigonometric expression is equal to another? I’m not exactly sure how to start.
start by using the most basic identities:
tanx=sinx/cosx
sin^2x + cos^2x = 1
by dividing by cos^2x you get
tan^2x+1 = sec^2x
divide by sin^2x and you get
1+cot^2x = csc^2x
There should be a section in your text covering trig identities. It will start out with simple ones like these and move on to more complicated ones.
Okay, thank you Steve!
To show that one trigonometric expression is equal to another, you would typically use trigonometric identities or properties to simplify and manipulate the expressions until they are in the same form.
Here is a step-by-step approach you can follow:
1. Start by examining both expressions and identifying any trigonometric identities that can be applied. Trigonometric identities are equations involving trigonometric functions that are true for all values of the variables involved.
2. Apply these identities to manipulate both sides of the equation in order to simplify them. You can utilize identities such as Pythagorean identities, sum and difference identities, double angle identities, or reciprocal identities. The goal is to make the expressions look as similar as possible.
3. Use basic algebraic manipulations, such as factoring, combining like terms, or expanding expressions, to further simplify both sides of the equation. Remember to keep the expressions equivalent at each step.
4. Keep simplifying both sides of the equation until you eventually arrive at a point where the expressions on both sides match exactly or can be proven to be equal. This typically involves breaking down complex trigonometric functions into simpler ones, canceling terms, or substituting identities repeatedly.
5. Finally, state the step-by-step transformations explicitly, showing how each expression was manipulated to become the other. This provides a clear and logical explanation for why the two expressions are equal.
Note that when working with trigonometric identities, it is important to remember the restrictions on the domain of the functions involved, as certain identities might not hold for all values of the variables.