Question

Simplify: cos(θ) * csc(θ) / sin(θ) * cot(θ)

a) 1
b) cos(θ)
c) sin(θ)
d) tan(θ)

Answer 1

The expression cos(θ) * csc(θ) / sin(θ) * cot(θ) simplifies to 1 after canceling out the sine and cosine terms, so the correct answer is (a) 1.

Step-by-step explanation:

The question asks us to simplify the expression: cos(θ) * csc(θ) / sin(θ) * cot(θ).

Let's simplify the expression step by step. The cosecant function, csc(θ), is the reciprocal of the sine function, so csc(θ) = 1/sin(θ). Likewise, the cotangent function, cot(θ), is the reciprocal of the tangent function, which is sin(θ)/cos(θ). Cotangent can also be written as cos(θ)/sin(θ).

Substituting these into the given expression, we get: cos(θ) * (1/sin(θ)) / (sin(θ) * (cos(θ)/sin(θ)))

Which simplifies to: (cos(θ)/sin(θ)) * (sin(θ)/cos(θ))

Since the cosines and sines cancel out respectively, we are left with: 1

Therefore, the correct answer is (a) 1.