If tanθ - cotθ = cosecθ, 0o < θ < 90o, then what is the value of (2tanθ - cosθ)/(√(3)cotθ + secθ) ?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. (4√3 - 1)/(6).
| Understanding/Application |
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tanθ - cotθ = cosecθ tanθ - 1/tanθ = cosecθ tan2θ - 1= tanθcosecθ sec2θ - 1 - 1 = secθ sec2θ - secθ - 2 = 0 sec2θ - 2secθ + secθ - 2 = 0 secθ(secθ - 2) + 1(secθ - 2) = 0 (secθ + 1) (secθ - 2) = 0 From, 00 < θ < 900 secθ = 2 cosθ = 1/2 θ = 600 |
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(2tanθ - cosθ)/(√(3)cotθ + secθ) = (2tan60 - cos60)/(√(3)cot60 + sec60) = (2√3 - 1/2)/(√3 × 1/√3 + 2) = (4√3 - 1)/6 |