Question

sec\(^2 23^\circ\) - tan\(^2 23^\circ\) + 2 =

• A. 0
• B. 1
• C. 2
• D. 3

Hint:

Use the identity \( \sec^2 \theta - \tan^2 \theta = 1 \) to simplify expressions in trigonometry. This helps in quickly resolving expressions that involve secant and tangent squares.

Answer 1

The Correct Option is D

Step 1: Use the Pythagorean identity: \[ \sec^2 \theta - \tan^2 \theta = 1 \] Step 2: Substituting \( \theta = 23^\circ \) into the identity: \[ \sec^2 23^\circ - \tan^2 23^\circ = 1 \] Step 3: Now, adding 2 to both sides: \[ \sec^2 23^\circ - \tan^2 23^\circ + 2 = 1 + 2 = 3 \] Thus, the correct answer is \( \boxed{3} \).