Question

Use basic identities to simplify the expression tan(θ)/cot(θ)?

Answer 1

To simplify the expression tan(θ)/cot(θ), replace cot(θ) with 1/tan(θ), which simplifies to tan2(θ).

Step-by-step explanation:

The student has been asked to simplify the expression tan(θ)/cot(θ) using basic trigonometric identities. To simplify this expression, we need to recall that the cotangent function is the reciprocal of the tangent function, which can be written as cot(θ) = 1/tan(θ). Therefore, when simplifying tan(θ)/cot(θ), we substitute cot(θ) with its equivalent 1/tan(θ).

The simplification proceeds as follows:

• tan(θ)/cot(θ) = tan(θ) × (1/cot(θ))
• tan(θ)/cot(θ) = tan(θ) × tan(θ)
• tan(θ)/cot(θ) = tan2(θ)

Thus, the simplified expression is tan2(θ).