2021 · Q57
If for some θ lying between 0° and 90°, tanθ = 1, then what is the value of sin²θ − 2sinθcosθ ?
Elementary MathematicsTrigonometry
- A−1
- B0
- C1/2
- D−1/2
Explanation
tanθ = 1 with 0° < θ < 90° gives θ = 45°, so sinθ = cosθ = 1/√2. Then sin²θ − 2sinθcosθ = 1/2 − 2·(1/2) = −1/2. This is option (d).