2022 · Q60
If (cosθ)/(cscθ+1)+(cosθ)/(cscθ-1)=2 where 0 < θ<90°, then what is the value of sin⁴θ+cos⁴θ?
Elementary MathematicsTrigonometry
- A2
- B1
- C1/2
- D1/4
Explanation
Combining the fractions: cosθ[2cscθ/(csc²θ-1)] = 2tanθ = 2, so θ = 45°. Then sin⁴θ+cos⁴θ = 1/4+1/4 = 1/2. Hence the keyed option is C.