hms.tech said:Homework Statement
Show that :
1 + cos(2∏/5)= 2 cos(∏/5)
Hello sacscale. Welcome to PF !sacscale said:Looks like the identity should have been:
1 + cos(2∏/5) = 2 cos^2(∏/5)
Assuming you are trying to prove 1 + cos(2##\pi##/5) = cos2(##\pi##/5) rather than what you originally posted, rewrite the left side using the double angle identity.hms.tech said:Yes but the issue remains, how do we prove it ?
A trigonometric identity is an equation that is true for all values of the variables involved. It is usually expressed in terms of sine, cosine, and tangent functions.
To prove a trigonometric identity, you must manipulate the equation using algebraic and trigonometric properties until both sides of the equation are equal. You can also use known trigonometric identities to help with the proof.
Some common trigonometric identities include the Pythagorean identities, double angle identities, half angle identities, and sum and difference identities. These can be used to simplify or prove more complex trigonometric equations.
Proving trigonometric identities helps to strengthen our understanding of trigonometry and its applications. It also allows us to solve more complex equations and problems in mathematics, physics, and engineering.
Some tips for proving trigonometric identities include starting with the more complex side of the equation, using common identities to simplify, and making sure to use correct algebraic and trigonometric properties. It is also helpful to practice and familiarize yourself with common identities.