Question

The value of \[ 1+\cot^2 30^\circ-\sec^2 45^\circ \] is

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

Hint:

Memorize the standard trigonometric values for \(30^\circ\), \(45^\circ\), and \(60^\circ\). They are frequently used in simplification problems.

Answer 1

The Correct Option is C

Step 1: Recall standard values.
\(\cot30^\circ=\sqrt{3}\), \(\sec45^\circ=\sqrt{2}\).

Step 2: Substitute directly.
\(1+\cot^230^\circ-\sec^245^\circ=1+3-2=2\). \[ \boxed{2} \]