2022 · Q46
x = (1-cos θ +sinθ )/(1+sinθ ) then what is (sin θ + cosθ -1)/(cosθ ) equal to?
Elementary MathematicsTrigonometry
- A1/x
- Bx
- C1 + x
- Dx - 1
Explanation
Cross-multiplication verifies (1-cosθ+sinθ)cosθ = (1+sinθ)(sinθ+cosθ-1); both sides equal cosθ-cos²θ+sinθcosθ. Hence (sinθ+cosθ-1)/cosθ equals x. Hence the keyed option is B.