Question

The following trigonometric equation is considered to be a trigonometric identity: cos(x°) = sin(90 - x°) Using complete sentences, explain why an infinite number of x values that will prove the trigonometric identity to be true.

Answer 1

The trigonometric equation cos(x°) = sin(90 - x°) is considered a trigonometric identity because it holds true for all values of x. By using definitions and trigonometric identities, we can prove that LHS = RHS, showing that the identity is true for infinite x values.

Step-by-step explanation:

The given trigonometric equation, cos(x°) = sin(90 - x°), is a trigonometric identity because it holds true for all values of x. To prove this, we can use the definitions of sine and cosine functions and apply trigonometric identities. Let's substitute the values and simplify each side of the equation:

Left-hand side (LHS): cos(x°)

Right-hand side (RHS): sin(90 - x°)

Using the angle sum identity for sine, sin(90 - x°) can be rewritten as sin(90)cos(x°) - cos(90)sin(x°), which simplifies to cos(x°).

Therefore, LHS = RHS, and the identity is proven true for all x values. Since there are infinite values of x, there are an infinite number of x values that will prove the trigonometric identity to be true.