Solving the Mystery of an Unfamiliar Trig Identity

• thenewbosco
In summary, a trig identity is a mathematical expression that equates two different trigonometric functions and is always true for any value of the variables involved. To solve an unfamiliar trig identity, you can use known trig identities, algebraic manipulation, and the properties of trigonometric functions. While a calculator can assist with computations, it is important to understand the concepts and techniques involved in solving trig identities. Solving trig identities is crucial in various fields such as engineering, physics, and mathematics, as it allows for simplification of complex equations and solving real-world problems. Some tips for solving trig identities include identifying known identities, using algebraic manipulation, and substituting values for variables to check their validity.
thenewbosco
Today the professor wrote down the following for use in an integral:

$$\frac{1}{2}cos(2\theta)=sin\theta cos\theta$$

i am not sure is this is correct. i have tried to prove this and cannot, i have also not found it in an table of trig identities. Is this a valid identity? i am not sure since this prof always makes mistakes

It should be $$\frac{1}{2}\sin 2\theta = \sin\theta \cos\theta$$

He probably meant

$$\int \cos 2\theta = \sin\theta \cos\theta +c$$

Daniel.

1. What is a trig identity?

A trig identity is a mathematical expression that equates two different trigonometric functions and is always true for any value of the variables involved.

2. How do I solve an unfamiliar trig identity?

To solve an unfamiliar trig identity, you can use known trig identities, algebraic manipulation, and the properties of trigonometric functions to simplify the expression and eventually prove that both sides are equal.

3. Can I use a calculator to solve a trig identity?

While a calculator can help with computations, it is not recommended to solely rely on it for solving trig identities. It is important to understand the concepts and techniques involved in solving them.

4. What is the importance of solving trig identities?

Solving trig identities is crucial in various fields such as engineering, physics, and mathematics. It allows for simplification of complex equations and the ability to manipulate them to solve real-world problems.

5. Are there any tips for solving trig identities?

Some tips for solving trig identities include identifying known identities, using algebraic manipulation to simplify the expression, and substituting values for variables to check the validity of the identity.

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