Question
Download Solution PDFसमीकरण sin 2x + cos x = 0 का सामान्य हल ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
निम्न का सामान्य हल:
cos x = cos y ⇒ x = 2nπ ± y
sin x = sin y ⇒ x = nπ + (-1)ny
गणना:
दिए गए समीकरण को इस प्रकार हल किया जा सकता है:
sin 2x + cos x = 0
⇒ 2 sin x cos x + cos x = 0
⇒ cos x (2 sin x + 1) = 0
⇒ cos x = 0 या (2 sin x + 1) = 0
⇒ cos x = cos π/2 या sin x = sin (-π/6)
⇒ x = 2nπ +- π/2 OR x = nπ + (-1)n × (-π/6)
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