2022 · Q57
If (1)/(cosecθ -cotθ )-(1)/(sinθ )=x, then what is (1)/(cosecθ +cotθ )-(1)/(sinθ ) equal to, where 0 < θ < (π )/(2)?
Elementary MathematicsTrigonometry
- A-x
- Bx
- C1/x
- D-1/x
Explanation
1/(cosecθ−cotθ) = sinθ/(1−cosθ); subtracting 1/sinθ gives cosθ/sinθ = cotθ, so x = cotθ. Likewise 1/(cosecθ+cotθ) − 1/sinθ = −cotθ = −x. The keyed option is A.