If (cosθ + sinθ) : (cosθ–sinθ) = (√3 + 1) : (√3 – 1),0° < θ 90°, then what is the value of secθ?
If (cosθ + sinθ) : (cosθ–sinθ) = (√3 + 1) : (√3 – 1),0° < θ 90°, then what is the value of secθ? Correct Answer (2√3)/3
(cosθ + sinθ)/(cosθ – sinθ) = (√3 + 1)/( √3 – 1)
Using dividendo and componendo,
⇒ (cosθ + sinθ + cosθ – sinθ)/(cosθ + sinθ – cosθ + sinθ) = (√3 + 1 + √3 – 1)/( √3 + 1 - √3 + 1)
⇒ 2cosθ/2sinθ = 2√3/2
⇒ cotθ = √3
⇒ cotθ = cot30
⇒ θ = 30
Now,
⇒ sec θ = sec 30 = 2/√3 = 2√3/3
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Feb 20, 2025