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Question

If in a ABC, 4 tanA+3=0 then sinA2 and cosA2 are the roots of

A
10x2410x+3=0
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B
10x2+410x+3=0
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C
10x2410x3=0
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D
10x2+410x3=0
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Solution

The correct option is A 10x2410x+3=0

tanA=34.
Hence
sinA=35 and cosA=45.
Then
cosA2=1+cosA2

=910

=310 ...(i)
And
sin(A2)=1cosA2

=110.
Hence
Sum of roots =410
And
Product of roots =310.
Hence the correct answer is option A.


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