If p(√3 + cot 30°) = tan³60° − 2sin60°, then the value of p is:

Correct — B. Substitute the standard angle values, then divide.

cot 30° = √3, so the bracket is √3 + √3 = 2√3
tan 60° = √3, so tan³60° = (√3)³ = 3√3
2 sin 60° = 2 × √3⁄2 = √3

Right side = 3√3 − √3 = 2√3
So p × 2√3 = 2√3, and dividing both sides by 2√3 gives p = 1

That is option (b), which prints the numeral 1.

Why the others are wrong

• (a)
  Option (a) shows √3. Put p = √3 and the left side becomes √3 × 2√3 = 6, while the right side is 2√3 ≈ 3.46 — the two sides do not balance.
• (c)
  Option (c) shows −1. The subtraction removes the smaller term (√3 from 3√3), so the right side stays positive and p cannot carry a minus sign.
• (d)
  Option (d) shows 2√3, which is the value of the right-hand side itself. You land there by simplifying 3√3 − √3 and then forgetting to divide by the bracket.

Three entries of the exact-value table decide this item: cot 30° = √3, tan 60° = √3 and sin 60° = √3⁄2.

Once those are in, both sides are multiples of the same surd, and the equation collapses to a division rather than any identity work.

The notation matters as much as the values. tan³60° means (tan 60°)³, the ratio cubed — not tan of 180°. Cubing √3 gives 3√3, which is what makes the right side 2√3 and the answer a clean 1.

Key facts

• cot 30° = √3 and tan 60° = √3, so both appear as the same surd in this stem.
• sin 60° = √3⁄2, which makes 2 sin 60° equal to √3.
• tan³60° means (tan 60°)³ = (√3)³ = 3√3, not tan of a tripled angle.

Common traps

• Using cot 30° = 1⁄√3, which is the value of tan 30°
• Reading tan³60° as tan 180° and getting zero
• Stopping at the right-hand side of 2√3 without dividing by the bracket

No directly related past PYQ was found.