Value of tan 45° is

Question

Value of tan 45° is

1. A. 0
2. B. infinity
3. C. 1 (Correct answer)
4. D. √3/2

Correct Answer

Option C — 1

Detailed Solution & Explanation

The correct answer is 1.

Key Points

• tan 45° = 1, because in a right-angled isosceles triangle the perpendicular and base are equal, and tan θ = perpendicular ÷ base.
• Equivalently, tan 45° = sin 45° ÷ cos 45° = (1/√2) ÷ (1/√2) = 1.

Additional Information

• The standard table worth memorising:
  • sin: 0, 1/2, 1/√2, √3/2, 1 for 0°, 30°, 45°, 60°, 90°
  • cos: the same values in reverse order
  • tan: 0, 1/√3, 1, √3, undefined
• tan 90° is undefined, not infinity, because cos 90° = 0 and division by zero has no value.
• A quick check: tan increases steadily from 0 at 0°, so passing through exactly 1 at the midpoint 45° is expected.