Multiple choice

If (\sec\theta = \frac{65}{63}) and (\theta) is an acute angle, then the value of (8(\csc\theta - \cot\theta)) is:

  1. 4

  2. 1

  3. 8

  4. 2
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B Correct answer
Explanation

Given sec θ = 65/63, we find cos θ = 63/65. Using sin²θ = 1 - cos²θ, we get sin θ = 16/65. Then csc θ = 65/16 and cot θ = cos θ/sin θ = 63/16. Therefore csc θ - cot θ = (65-63)/16 = 2/16 = 1/8, and 8(csc θ - cot θ) = 1.

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