Question

Find the value of \(\frac{\sqrt{3} \cos 23^\circ - \sin 23^\circ}{2}\)

• A. \(\tan 53^\circ\)
• B. \(\sin 53^\circ\)
• C. 1
• D. \(\cos 53^\circ\)

Hint:

Use trigonometric identities to simplify and solve complex trigonometric expressions.

Answer 1

The Correct Option is A

We use the identity \(\tan (A - B) = \frac{\sin A \cos B - \cos A \sin B}{\cos A \cos B}\) to simplify the expression: \[ \frac{\sqrt{3} \cos 23^\circ - \sin 23^\circ}{2} = \tan 53^\circ \] Thus, the correct answer is \(\tan 53^\circ\).