Question
Download Solution PDFবক্ররেখার নতি y = sin-1 (cos x) tan θ, তাহলে (0, π) ব্যবধানে θ এর মান কত হবে?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFঅনুসৃত ধারণা:
অনুসৃত সূত্র:
- cos-1 (cos x) = x
- sin-1 (sin x) = x
- বক্ররেখার ঢাল = tan θ = \(\rm \frac {dy}{dx}\)
গণনা:
প্রদত্ত: ঢাল = tan θ
y = sin-1 (cos x)
⇒ y = sin-1 (sin (π/2 -x))
⇒ y = π/2 – x (∵ sin-1 (sin x) = x)
x এর সাপেক্ষে উভয় পক্ষের পার্থক্য করে, আমরা পাই
\(\rm \frac {dy}{dx}\) = -1
আমরা জানি, ঢাল = \(\rm \frac {dy}{dx}\)
⇒ tan θ = -1
∴ θ = 3π/4
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