(Sinθ + Cosθ)/(Sinθ - Cosθ) = 7 হলে Secθ এর মান কত?
Solution
Correct Answer: Option B
দেয়া আছে,
(Sinθ + Cosθ)/(Sinθ - Cosθ) = 7
⇒ (Sinθ + Cosθ) + (Sinθ - Cosθ)/(Sinθ + Cosθ) - (Sinθ - Cosθ) = (7 + 1)/(7 - 1)
[যোজন-বিয়োজন করে]
⇒ (Sinθ + Cosθ + Sinθ - Cosθ)/(Sinθ + Cosθ - Sinθ + Cosθ) = 8/6
⇒ 2Sinθ/2Cosθ = 4/3
⇒ Sinθ/Cosθ = 4/3
⇒ tanθ = 4/3
⇒ tan2θ = 16/9
⇒ Sec2θ - 1 = 16/9
⇒ Sec2θ = (16/9) + 1
⇒ Sec2θ = (16 + 9)/9
⇒ Sec2θ = 25/9
∴ Secθ = ±5/3
(Sinθ + Cosθ)/(Sinθ - Cosθ) = 7
⇒ (Sinθ + Cosθ) + (Sinθ - Cosθ)/(Sinθ + Cosθ) - (Sinθ - Cosθ) = (7 + 1)/(7 - 1)
[যোজন-বিয়োজন করে]
⇒ (Sinθ + Cosθ + Sinθ - Cosθ)/(Sinθ + Cosθ - Sinθ + Cosθ) = 8/6
⇒ 2Sinθ/2Cosθ = 4/3
⇒ Sinθ/Cosθ = 4/3
⇒ tanθ = 4/3
⇒ tan2θ = 16/9
⇒ Sec2θ - 1 = 16/9
⇒ Sec2θ = (16/9) + 1
⇒ Sec2θ = (16 + 9)/9
⇒ Sec2θ = 25/9
∴ Secθ = ±5/3
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