Question

Find (1 - cos² θ)(cot²θ + 1) - 1.

• A. sec²θ
• B. 0
• C. 2
• D. -2

Answer 1

Answer:

B. 0

Let's simplify the expression step-by-step:

1. Use the Pythagorean identity:

   • 1 - cos²θ = sin²θ

2. Use the trigonometric identity:

   • cot²θ + 1 = csc²θ

3. Substitute these identities into the expression:

   • (1 - cos²θ)(cot²θ + 1) - 1 = (sin²θ)(csc²θ) - 1

4. Use the reciprocal identity:

   • csc²θ = 1/sin²θ

5. Substitute this into the expression:

   • (sin²θ)(1/sin²θ) - 1

6. Simplify:

   • 1 - 1 = 0

Therefore, (1 - cos² θ)(cot²θ + 1) - 1 = 0.