Then, to find a half angle identity for tangent, we just use the fact that and plug in the half angle identities for sine and cosine.
is an equation that involves trigonometric functions and is true for every single value substituted for the variable (assuming both sides are "defined" for that value) You will find that trigonometric identities are especially useful for simplifying trigonometric expressions.
The next set of fundamental identities is the set of reciprocal identities, which, as their name implies, relate trigonometric functions that are reciprocals of each other. We see only one graph because both expressions generate the same image. This is a good way to confirm an identity verified with analytical means.
If both expressions give the same graph, then they are most likely identities. In the second method, we split the fraction, putting both terms in the numerator over the common denominator.
We will begin with the Pythagorean identities (see [link]), which are equations involving trigonometric functions based on the properties of a right triangle.
We have already seen and used the first of these identifies, but now we will also use additional identities.
They are the basic tools of trigonometry used in solving trigonometric equations, just as factoring, finding common denominators, and using special formulas are the basic tools of solving algebraic equations.
In fact, we use algebraic techniques constantly to simplify trigonometric expressions.
As long as the substitutions are correct, the answer will be the same.
We have seen that algebra is very important in verifying trigonometric identities, but it is just as critical in simplifying trigonometric expressions before solving.