What is the value of (cos 40° – cos 140°)/(sin 80° + sin 20°)?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 2/√3
= (cos 40° – cos 140°)/(sin 80° + sin 20°)
= [2sin{(40° + 140°)/2} sin{(140° - 40°)/2}]/[2sin {(80° + 20°)/2} cos{(80° - 20°)/2}]
= (2sin90°sin50°)/(2sin50°cos30°) = sin90°/cos30° = 1/(√3/2) = 2/√3