Question
Download Solution PDFमान लीजिए वक्र y = sin-1 (cos x) का ढलान tan θ है, तो अंतराल (0, π) में θ का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
सूत्र:
- cos-1 (cos x) = x
- sin-1 (sin x) = x
- वक्र का ढलान = tan θ =
गणना:
दिया गया है: ढलान = tan θ
y = sin-1 (cos x)
⇒ y = sin-1 (sin (π/2 -x))
⇒ y = π/2 – x (∵ sin-1 (sin x) = x)
x के संबंध में दोनों पक्षों का अवकलन करने पर, हमें निम्न प्राप्त होता है
चूँकि हम जानते हैं, ढलान =
⇒ tan θ = -1
∴ θ = 3π/4
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