What is an identity

The video tutorial explains the concept of identities in mathematics, starting with basic examples like 1=1 and a-a=0. It discusses the importance of ensuring both sides of an equation are equivalent to establish an identity. The tutorial also covers famous identities, such as a*1/a=1, and delves into verifying identities using algebraic and trigonometric expressions. The key takeaway is understanding that identities hold true regardless of the values plugged into the variables, ensuring both sides of the equation remain equal.

What is the defining characteristic of an identity in mathematics?

• It is an equation where both sides are different.

• It is an equation where both sides are equivalent.

• It is an equation with no variables.

• It is an equation that cannot be solved.

Which of the following is an example of an identity?

• a / b = c

• a - a = 0

• a + b = c

• a * b = c

How can the identity a * 1 / a = 1 be verified?

• By showing a * 1 = a

• By showing a / a = 1

• By showing a + 1 = a

• By showing a - 1 = 0

What is the trigonometric identity for tangent of theta?

• sine of theta times cosine of theta

• sine of theta over cosine of theta

• cosine of theta over sine of theta

• cosine of theta minus sine of theta

Why is verifying identities important in mathematics?

• To ensure both sides of an equation are different

• To confirm that both sides of an equation are equivalent

• To find the value of unknown variables

• To simplify complex equations