Question
Download Solution PDFयदि sin θ + cos θ = \(\sqrt5\) sin(90 - θ) है, तो cot θ का मान ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
sin θ + cos θ = \(\sqrt5\) sin(90 - θ)
प्रयुक्त अवधारणा:
1. cot θ = cos θ ÷ sin θ
2. a2 - b2 = (a + b)(a - b)
गणना:
sin θ + cos θ = \(\sqrt5\) sin(90 - θ)
⇒ sin θ + cos θ = \(\sqrt5\) cosθ
⇒ cos θ(\(\sqrt5\) - 1) = sinθ
⇒ cot θ = \(\frac {1}{\sqrt5 - 1}\)
⇒ cot θ = \(\frac {\sqrt5 + 1}{(\sqrt5 - 1)(\sqrt5 + 1)}\)
⇒ cot θ = \(\frac {\sqrt5 + 1}{5 - 1}\)
⇒ cot θ = \(\frac {\sqrt5 + 1}{4}\)
∴ cot θ का मान \(\frac {\sqrt5 + 1}{4}\) है।
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