2017 · Q64
What is the value of sin x √(1/(1+cos x) + 1/(1−cos x)) ?
Elementary MathematicsTrigonometry
- A√(2)
- B2√(2)
- C√(2) tan x
- D0
Explanation
1/(1+cosx) + 1/(1−cosx) = 2/(1−cos²x) = 2/sin²x. So the expression is sinx·√2/|sinx| = √2 (for sinx > 0): option A. Option B (2√2) doubles the numerator.