2015 · Q40
If θ is an acute angle and sin θ cos θ = 2 cos³ θ − 1.5 cos θ, then what is sin θ equal to?
Elementary MathematicsStatistics
- A(√5 − 1)/4
- B(1 − √5)/4
- C(√5 + 1)/4
- D−(√5 + 1)/4
Explanation
Dividing by cos: sin = 2cos^2 - 3/2 = 1/2 - 2sin^2, i.e. 4sin^2 + 2sin - 1 = 0. The acute root is sin = (sqrt(5) - 1)/4. Hence option (a).