Question

The value of cos 1200° + tan 1485° is

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

Answer 1

The Correct Option is A

Let's break down the trigonometric expressions:

1. For \( \cos 120^\circ \): \( \cos 120^\circ = -\frac{1}{2} \), since \( \cos 120^\circ \) lies in the second quadrant where cosine is negative.
2. For \( \tan 1485^\circ \): First, reduce the angle \( 1485^\circ \) to an angle between 0° and 360°: \[ 1485^\circ \div 360^\circ = 4 \text{ full circles with remainder } 1485 - 4 \times 360 = 1485 - 1440 = 45^\circ. \] Thus, \( \tan 1485^\circ = \tan 45^\circ = 1 \), since \( \tan 45^\circ = 1 \).

So, we have: \[ \cos 120^\circ + \tan 1485^\circ = -\frac{1}{2} + 1 = \frac{1}{2}. \]

The correct answer is (A) : \(\frac 12.\)