Maths · Trigonometrical identities and trigonometrical functions
If a is any real number, the number of roots of in the first quardrant is
If a is any real number, the number of roots of \( \cot x-\tan x=a \) in the first quardrant is
- A. 2
- B. 0
- C. 1
- D. 4
Step-by-step solution
Simplify cot x - tan x to 2 cot 2x. The equation becomes cot 2x = a/2. For x in first quadrant (0, π/2), 2x ∈ (0, π). cot θ is a bijection from (0, π) to ℝ, so exactly one θ satisfies cot θ = a/2, giving one x.
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