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Question

If cosα is a root of 25x2+5x12=0 and (1<x<0), then the value of tan2α can be:

A
2412
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B
1224
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C
2024
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D
247
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Solution

The correct option is C 247
cosα is a root of the given equation.
25cos2α+5cosα12=0(5cosα+4)(5cosα3)=0cosα=[45,35]tanα=±1cos2αcosα=±1162545=±34
We reject the negative value as tanα is positive within the given range of x.
Now,
tan2α=2tanα1tan2α=2×341916=247
Ans: Option D.

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