Multiple choice

If ( \tan (2\theta + 45^o) = \cot 3\theta ) where ( (2\theta + 45^o) ) and ( 3\theta ) are acute angles, then the value of ( \theta ) is -

  1. $5^o$
  2. $9^o$
  3. $12^o$
  4. $15^o$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the complementary angle relationship: if tan(A) = cot(B), then A + B = 90°. Substituting: (2θ + 45°) + 3θ = 90°, so 5θ = 45°, giving θ = 9°. Verify: tan(2×9° + 45°) = tan(63°) and cot(3×9°) = cot(27°), and since 63° + 27° = 90°, they are equal.

Keep practicing — related questions