Can Trig Identities Be Proven Using Basic Trigonometric Functions?

Thread starter ttpp1124
Start date May 11, 2020
Tags

identities Trig Trig identities

In summary, proving trigonometric identities is important for manipulating and simplifying complicated expressions. The process involves using algebraic and trigonometric properties to equate both sides of the equation. Commonly used identities include Pythagorean, double angle, and sum and difference identities. Tips for solving difficult identities include simplifying, rewriting, and factoring. Common mistakes to avoid include forgetting parentheses, dividing by zero, and not simplifying both sides of the equation. Double checking your work is also crucial.

May 11, 2020

ttpp1124

Homework Statement: I believed I've proved it right, but can someone confirm?

Relevant Equations: n/a

Physics news on Phys.org

May 11, 2020

member 587159

I believe it is correct, but note that

$$(\tan^2 x -1)/\sec^2 x = (\tan^2 x -1) \cos^2 x = \sin^2 x - \cos^2 x = - \cos(2x)$$

so you could have been a little faster.

1. Can trig identities be proven using only basic trigonometric functions?

Yes, trigonometric identities can be proven using only basic trigonometric functions such as sine, cosine, and tangent. These functions are the building blocks of trigonometry and can be used to derive more complex identities.

2. How do you prove a trig identity using basic trigonometric functions?

To prove a trigonometric identity using basic trigonometric functions, you can use algebraic manipulation, substitution, or the use of trigonometric identities such as the Pythagorean identities.

3. Are there any shortcuts for proving trig identities using basic trigonometric functions?

Yes, there are some shortcuts that can be used when proving trigonometric identities. These include using symmetry, converting all trigonometric functions to sine and cosine, and using double angle or half angle identities.

4. Can all trig identities be proven using basic trigonometric functions?

Yes, all trigonometric identities can be proven using basic trigonometric functions. However, some identities may require more steps and manipulations than others.

5. Why is it important to be able to prove trig identities using basic trigonometric functions?

Proving trigonometric identities using basic trigonometric functions is important as it helps to deepen our understanding of trigonometry and its fundamental concepts. It also allows us to solve more complex trigonometric equations and problems.