To simplify the expression cotθ/cotθsecθcotθ1cot^2θtanθ, we can start by simplifying each term individually.

1. Simplify cotθ/cotθ:
The cotθ term in the numerator cancels out with the cotθ term in the denominator, leaving us with 1.

2. Simplify secθ:
The reciprocal of secθ is cosθ, so we can rewrite secθ as 1/cosθ.

3. Simplify cotθ1:
The product of cotθ and 1 is simply cotθ.

4. Simplify cot^2θ:
The square of cotθ is equal to (1/tanθ)^2, which simplifies to 1/tan^2θ.

5. Simplify tanθ:
The reciprocal of tanθ is 1/cotθ, so we can rewrite tanθ as 1/cotθ.

Now, let's substitute these simplified terms back into the original expression:

1 / (1/cosθ * cotθ * 1/tan^2θ * 1/cotθ)

Next, we can simplify the expression further by multiplying the fractions:

1 * cosθ * tan^2θ * cotθ

Finally, we can simplify the expression by rearranging the terms:

cosθ * tan^2θ * cotθ

Therefore, the simplified expression is cosθ * tan^2θ * cotθ.

Question

To simplify the expression cotθ/cotθsecθcotθ1cot^2θtanθ, we can start by simplifying each term individually.

1. Simplify cotθ/cotθ:
   The cotθ term in the numerator cancels out with the cotθ term in the denominator, leaving us with 1.

2. Simplify secθ:
   The reciprocal of secθ is cosθ, so we can rewrite secθ as 1/cosθ.

3. Simplify cotθ1:
   The product of cotθ and 1 is simply cotθ.

4. Simplify cot^2θ:
   The square of cotθ is equal to (1/tanθ)^2, which simplifies to 1/tan^2θ.

5. Simplify tanθ:
   The reciprocal of tanθ is 1/cotθ, so we can rewrite tanθ as 1/cotθ.

Now, let's substitute these simplified terms back into the original expression:

1 / (1/cosθ * cotθ * 1/tan^2θ * 1/cotθ)

Next, we can simplify the expression further by multiplying the fractions:

1 * cosθ * tan^2θ * cotθ

Finally, we can simplify the expression by rearranging the terms:

cosθ * tan^2θ * cotθ

Therefore, the simplified expression is cosθ * tan^2θ * cotθ.

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