If 5 sin2θ + 14cosθ = 13, 0o < θ < 90o, then what is the value of (secθ + cotθ)/(cosecθ + tanθ) ?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e 31/29.
| Understanding/Application |
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5sin2θ + 14cosθ = 13 5 (1 - cos2θ) + 14cosθ - 5cos2θ + 14cosθ = 8 5cos2θ - 10cosθ - 4cosθ + 8 = 0 5cosθ (cosθ - 2) - 4(cosθ - 2) = 0 (5cosθ - 4) (cosθ - 2) = 0 (cosθ - 2) = 0 (It is not possible) For 00 < θ < 900 (5cosθ - 4) = 0 cosθ = 4/5 by triplet, 3 - 4 - 5 sinθ = 3/5 |
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cosθ = 1/secθ sinθ = 1/cosecθ cotθ = cosθ/sinθ tanθ = sinθ/cosθ = (secθ + cotθ)/(cosecθ + tanθ) = (5/4 + 4/3)/(5/3 + 3/4) = (31/12)/(29/12) = 31/29 |