Question
Download Solution PDFsin⁴θ + cos⁴θ = 2sin²θcos²θ అయితే, 0°
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFఇవ్వబడింది:
sin⁴θ + cos⁴θ = 2sin²θcos²θ, 0°
ఉపయోగించిన సూత్రం:
sin²θ + cos²θ = 1
గణన:
sin²θ = x అనుకుందాం, అప్పుడు cos²θ = 1 - x
ఇవ్వబడిన సమీకరణం: sin⁴θ + cos⁴θ = 2sin²θcos²θ
⇒ x² + (1 - x)² = 2x(1 - x)
⇒ x² + 1 - 2x + x² = 2x - 2x²
⇒ 2x² + 1 - 2x = 2x - 2x²
⇒ 4x² - 4x + 1 = 0
⇒ (2x - 1)² = 0
⇒ 2x - 1 = 0
⇒ x = 1/2
⇒ sin²θ = 1/2
⇒ sin θ = 1/√2
⇒ cos θ = 1/√2
⇒ cot θ = cos θ / sin θ = (1/√2) / (1/√2) = 1
కాబట్టి, సరైన సమాధానం 3వ ఎంపిక.
Last updated on Jun 17, 2025
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