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Solve the following equations:2cos 2x – 7 cos x + 3 = 0 - Mathematics

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प्रश्न

Solve the following equations:
2cos 2x – 7 cos x + 3 = 0

योग
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उत्तर

2 cos2x – 7 cos x + 3 = 0

2 cos2x – 6 cos x – cos x + 3 = 0

2 cos x (cos x – 3) – 1(cos x – 3) = 0

(2 cos x – 1)(cos x – 3) = 0

2 cos x – 1 = 0 or cos x – 3 = 0

cos x = `1/2` or cos x = 3|

Since – 1 ≤ cos x ≤ 1, we have

cos x = 3 is not possible.

∴ cos x = `1/2`

cos x = `cos  pi/3`

The general solution is x = `2"n"pi +- pi/3`, n ∈ Z

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  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Trigonometry - Exercise 3.8 [पृष्ठ १३३]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
अध्याय 3 Trigonometry
Exercise 3.8 | Q 3. (xi) | पृष्ठ १३३

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