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Question
Find A, if 0° ≤ A ≤ 90° and 2 cos2 A + cos A – 1 = 0
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Solution
2 cos2 A + cos A – 1 = 0
`=>` 2 cos2 A + 2 cos A – cos A – 1 = 0
`=>` 2 cos A (cos A + 1) – 1(cos A + 1) = 0
`=>` (2 cos A – 1)(cos A + 1) = 0
`=>` cos A = `1/2` or cos A = –1
We know `cos 60^circ = 1/2`
We also know that for no value of A(0° ≤ A ≤ 90°), cos A = –1.
Hence, A = 60°
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