If 12 cot2 θ – 31 cosec θ + 32 = 0, then value of sin θ is1. \(\

1.	If 12 cot2 θ – 31 cosec θ + 32 = 0, then value of sin θ is1. \(\frac{3}{5}\) or 12. \(\frac{2}{3}\) or \(\frac{-2}{3}\)3. \(\frac{4}{5}\) or \(\frac{3}{4}\)4. \(\pm\frac{1}{2}\)
Answer» 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

If 12 cot2 θ – 31 cosec θ + 32 = 0, then value of sin θ is1. \(\frac{3}{5}\) or 12. \(\frac{2}{3}\) or \(\frac{-2}{3}\)3. \(\frac{4}{5}\) or \(\frac{3}{4}\)4. \(\pm\frac{1}{2}\)

Answer»

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

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If 12 cot2 θ – 31 cosec θ + 32 = 0, then value of sin θ is1. \(\frac{3}{5}\) or 12. \(\frac{2}{3}\) or \(\frac{-2}{3}\)3. \(\frac{4}{5}\) or \(\frac{3}{4}\)4. \(\pm\frac{1}{2}\)

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