Multiple choice

What is the value of [1 - tan(90° - θ) + sec(90° - θ)]/[tan(90° - θ) + sec(90° - θ) + 1]?

  1. Cot(θ /2)

  2. Tan(θ /2)

  3. Sin θ

  4. Cos θ
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using complementary angle identities: tan(90° - θ) = cot θ, sec(90° - θ) = cosec θ. Expression becomes [1 - cot θ + cosec θ]/[cot θ + cosec θ + 1]. Using cosec² θ - cot² θ = 1, this simplifies to [cosec θ - cot θ]/[cosec θ + cot θ]. Writing in terms of half angles: this equals tan(θ/2).

Keep practicing — related questions