If 12 cot2θ – 31 cosec θ + 32 = 0, 0° < θ < 90°, then the values of sin θ will be:
Show answer & explanation
Correct answer: B
Explanation
Correct Answer is option 2 i.e. 4/5, 3/4
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Concept |
Understanding |
Application |
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cot2θ = cosec2θ– 1 cos2θ = 1 – sin2θ |
Given 12cot2θ – 31cosecθ + 32=0 0° <θ<90° |
12cot2θ – 31cosecθ + 32=0 ⇒ 12(cosec2θ– 1) – 31cosecθ + 32 = 0 ⇒ 12cosec2θ – 31cosecθ + 20 = 0 ⇒ 12cosec2θ– 16cosecθ– 15cosecθ + 20 = 0 ⇒ 4cosecθ(3cosec θ– 4) – 5(3cosec θ– 4) = 0 ⇒ (4cosecθ– 5) (3cosec θ– 4) = 0 ⇒ cosec θ = 5/4 or 4/3 ⇒ sin θ = 4/5 or 3/4 |