Question

Establish the identity.

(csc 0+1)(csc 0-1) = cot 0

a. Multiply and write the left side expression as the difference of two squares: ?

b. The expression from the previous step is equivalent to cot 0 using what?
OA. Cancellation Property
OB. Quotient Identity
OC. Pythagorean Identity
OD. Reciprocal Identity
OE. Even-Odd Identity

pls help asap i can’t pass this class without passing this test

Answer 1

To establish the given identity, we need to first multiply the left side of the equation and write it as the difference of two squares. This can be done by using the difference of squares formula, which states that the difference of two squares can be written as the product of the square of the sum and the square of the difference.

The left side of the given equation can be written as:

(csc0+1)(csc0-1)

We can then apply the difference of squares formula to this expression to get:

(csc0+1)(csc0-1) = (csc0+1)(csc0-1)

Now, we can see that this expression is equivalent to cot 0 using the Pythagorean Identity. This identity states that the sum of the squares of the cosecant and cotangent of an angle is equal to 1. In this case, since (csc0+1)(csc0-1) = cot 0, we can use the Pythagorean Identity to rewrite the left side of the equation as (csc0^2 + cot0^2) = 1, which is equivalent to cot 0.

Therefore, the given identity is established using the Pythagorean Identity. This means that the correct answer is C. Pythagorean Identity.