2023 · Q29
How many values of θ will satisfy the equation (sin²θ − 4sin θ + 3)(4 − cos²θ + 4sin θ) = 0, where 0 < θ < π/2?
Elementary MathematicsTrigonometry
- ANone
- BOnly one
- COnly two
- DOnly three
Explanation
sin^2-4sin+3=(sin-1)(sin-3)=0 gives sin=1 (theta=pi/2, excluded); second factor 4-cos^2+4sin=4-(1-sin^2)+4sin=(sin+? )... only sin=1 works, none in (0,pi/2). Option (a).