Practice30Create account

Given that tan15° = 2 − √3, the value of tan75° is:

Competition practiceTrigonometry
  • A√3 − 2
  • B(2 − √3)/2
  • C2 + √3
  • D−(2 + √3)

Step-by-Step Solution

75° and 15° are complementary, so tan75° = cot15° = 1/(2 − √3). Rationalising: 1/(2 − √3) × (2 + √3)/(2 + √3) = (2 + √3)/(4 − 3) = 2 + √3 ≈ 3.732. Negating instead of inverting gives √3 − 2.
Answer: C) 2 + √3

Master this topic in 30 minutes a day.

Don't just memorise the answer — build a daily practice habit.

Practice 5 Similar Questions Free →

All Trigonometry practice questions

More Trigonometry practice

The expression cos⁴θ − sin⁴θ + 1 is equal to:Which of the following is IMPOSSIBLE for a real angle θ?The shadow of a vertical tower on level ground is 15 m long when the sun's altitude is…If cosecθ = √5 and θ is acute, the value of (2 − sin²θ)/(1 + cot²θ) is:If sin⁴θ − cos⁴θ = 1/3, then sin²θ equals: