Question

Evaluate: \( 1 + \cot^2 30^\circ - \sec^2 45^\circ \)

• A. \( \frac{1}{4} \)
• B. \( \frac{1 - \sqrt{3}}{2} \)
• C. \( 2 \)
• D. \( 0 \)

Hint:

Trigonometric Evaluation}
Know standard values for \( \cot, \sec \) at \( 30^\circ, 45^\circ \)
Use \( \cot 30^\circ = \sqrt{3} \), \( \sec 45^\circ = \sqrt{2} \)
Always square the values carefully

Answer 1

The Correct Option is C

Recall: \[ \cot 30^\circ = \sqrt{3} \Rightarrow \cot^2 30^\circ = 3 \] \[ \sec 45^\circ = \sqrt{2} \Rightarrow \sec^2 45^\circ = 2 \] So, \[ 1 + \cot^2 30^\circ - \sec^2 45^\circ = 1 + 3 - 2 = 2 \]