Question

Determine whether the equation is an identity or not an identity.

cos theta / sin theta tan theta = 1

a. Identity
b. Not an identity

Answer 1

The given equation cos θ / (sin θ × tan θ) simplifies to cot² θ, which is not always equal to 1. Therefore, the equation is not an identity.

Step-by-step explanation:

The question asks to determine whether the equation cos θ / (sin θ × tan θ) = 1 is an identity or not. To verify this, we can use the trigonometric identity tan θ = sin θ / cos θ. Hence, if we plug tan θ into the original equation, we get cos θ / (sin θ × (sin θ / cos θ)), which simplifies to cos² θ / sin² θ. After further simplification, we get cos² θ / sin² θ = 1, which is not always true because the right side of the equation equals the cotangent squared, cot² θ, not 1. Therefore, the given equation is not an identity.