2019 · Q33
If 0 < θ < 90°, sin θ = 3/5 and x = cot θ, then what is the value of 1 + 3x + 9x² + 27x³ + 81x⁴ + 243x⁵?
Elementary MathematicsTrigonometry
- A941
- B1000
- C1220
- D1365
Explanation
sin.theta = 3/5 with theta acute gives cos.theta = 4/5, so x = cot.theta = 4/3. The sum is a GP: 1+3x+...+(3x)^5 = ((3x)^6-1)/(3x-1) = (4^6-1)/3 = 4095/3 = 1365.