2023 · Q52
What is the value of (1+cot²θ)(1+cosθ)(1-cosθ)-(1+tan²θ)(1+sinθ)(1-sinθ)?
Elementary MathematicsTrigonometry
- A-1
- B0
- C1
- D2
Explanation
(1 + cot²θ)(1 + cosθ)(1 − cosθ) = cosec²θ·sin²θ = 1, and (1 + tan²θ)(1 + sinθ)(1 − sinθ) = sec²θ·cos²θ = 1. Their difference is 1 − 1 = 0 (B).