Question

If 12 cot² θ – 31 cosec θ + 32 = 0, then value of sin θ is

1. \(\frac{3}{5}\) or 1

2. \(\frac{2}{3}\) or \(\frac{-2}{3}\)

3. \(\frac{4}{5}\) or \(\frac{3}{4}\)

4. \(\pm\frac{1}{2}\) 

Answer 1

 3. \(\frac{4}{5}\) or \(\frac{3}{4}\)

12 cot² θ - 31 cosec θ + 32 = 0

12 (cosec² θ - 1) - 31 cosec θ + 32 = θ

12 cosec² θ - 31 cosec θ + 20 = 0

12 cosec² θ - 16 cosec θ - 15 cosec θ + 20 = 0

4 cosec θ (3 cosec θ - 4 ) - 5 (3 cosec θ - 4) = 0

cosec θ = 5/4 or 4/3 ⇒ 4/5 or 3/4