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Question

The quadratic equation whose roots are cos218 and sin236 is

A
16x212x+1=0
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B
16x2+12x+1=0
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C
16x220x+5=0
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D
16x2+20x+5=0
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Solution

The correct option is C 16x220x+5=0
We have,
cos2180+sin2360=12[1+cos360+1cos720]=12[2+5+14514]=12[2+12]=54
Out of given options only Option C has sum of its roots as 5/4.
Product of roots cos2180+sin2360=14(sin540+sin180)2
=14(3+14+314)2
=14(32)2=516
Hence,
Option C is correct answer.

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