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If α is an cute angle and 2 sin α + 15 cos²α = 7 then the value of cot α is
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4 3 -
4 5 -
5 4 -
3 4
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Correct Option: D
2 sinα + 15 cos²α = 7
⇒ 2 sinα + 15 (1 – sin²α) = 7
⇒ 2 sinα + 15 – 15 sin²α = 7
⇒ 15 sin²α – 2 sinα – 15 + 7 = 0
⇒ 15 sin²α – 2 sinα – 8 = 0
⇒ 15 sin²α – 12 sinα + 10 sinα – 8 = 0
⇒ 3 sinα (5 sinα – 4) + 2 (5 sinα – 4) = 0
⇒ (3 sinα + 2) (5 sinα – 4) = 0
| ⇒ 5 sinα – 4 = 0 ⇒ sinα = | 5 |
| sinα ≠ - | because α is acute angle. 1 | 3 |
∴ cotα = √cosec²α - 1
