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Question

2sinαcosαsinαcosα is equal to

A
sec(α2π8)
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B
cos(π8α2)
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C
tan(α2π8)
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D
cot(α2π2)
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Solution

The correct option is D tan(α2π8)
2sinαcosαsinαcosα=2[112sinα12cosα]2[12sinα12cosα]=1[sin450sinα+cos450cosα]cos450sinαsin450cosα=1[cos(απ4)]sin(π4α)=2sin2(απ/42)2sin(π8α2)cos(π8α2)=tan(α2π8)

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