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Question


Find 10sin α if cosα satisfies the equation 25cos2α+5cosα12=0andπ/2<α<π.

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Solution

25cos2α+5cosα12=0
cosα=5±254(25)(12)50
=5±122550=0.6,0.8
α=53.13,143.13 αϵ(π2,π)
So only α=143.13 is taken.
cosα=0.8
hence sinα=0.6
sin2α=2sinαcosα
hence sin2α=-0.96

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