2016 · Q64
If p=cotθ+tanθ and q=secθ-cosθ, then (p²q)^(2/3)-(q²p)^(2/3) is equal to
Elementary MathematicsTrigonometry
- A0
- B1
- C2
- D3
Explanation
Here p = cotθ+tanθ = 1/(sinθcosθ) and q = secθ−cosθ = sin²θ/cosθ. Then p²q = 1/cos³θ and q²p = sin³θ/cos³θ. Subtracting the 2/3 powers gives 1/cos²θ − sin²θ/cos²θ = (1−sin²θ)/cos²θ = 1, option B.