2023 · Q26
What is the value of sin θ + cos θ, if θ satisfies the equation cot²θ − (√3 + 1)cot θ + √3 = 0; 0 < θ < π/4?
Elementary MathematicsTrigonometry
- A√2
- B2
- C(√3 + 1)/2
- D(√3 − 1)/2
Explanation
cot^2-(sqrt3+1)cot+sqrt3=0 gives cot=1 or sqrt3; with 0<theta<pi/4, cot>1 so cot=sqrt3, theta=pi/6, sin+cos=(1+sqrt3)/2. Option (c).