Use a sum or difference identity to find the exact value.
-cot x cos x + sin x = csc x
A)Not an Identity
B)Identity

Question

Quizplus · Accepted Answer

The given expression can be simplified using trigonometric identities. The cotangent function can be expressed as the reciprocal of the tangent function, or more relevantly here, as cos(x)/sin(x). Thus, the expression becomes (cos(x)/sin(x)) * cos(x) + sin(x). This simplifies to cos^2(x)/sin(x) + sin(x). Using the Pythagorean identity, cos^2(x) can be replaced with 1 - sin^2(x), leading to (1 - sin^2(x))/sin(x) + sin(x). This simplifies to 1/sin(x), which is the definition of csc(x), proving the statement is an identity.

Use a Sum or Difference Identity to Find the Exact