2025 · Q33
If (sinα -cosα )/(sinα +cosα ) where θ and α are (α ≠(π )/(4)) acute angles, then what is √2 sin θ equal to ?
Elementary MathematicsTrigonometry
- Asin α − cos α
- Bsin α + cos α
- Ccos α − sin α
- D± (sin α − cos α)
Explanation
The intended equation is tanθ = (sinα − cosα)/(sinα + cosα) with θ, α acute. Dividing numerator and denominator by cosα gives tanθ = (tanα − 1)/(tanα + 1) = tan(α − π/4), so θ = α − π/4. Then √2 sinθ = √2 sin(α − π/4) = sinα − cosα, option (a).