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Question

If sin2π8+sin23π8+sin25π8+sin27π8=m.Find m

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Solution

sin2π8+sin23π8+sin25π8+sin27π8
sin2π8+sin23π8+sin2(π2+π8)+sin2(π2+3π8)
sin2π8+sin23π8+cos25π8+cos27π8
(sin2π8+cos2π8)+(sin23π8+cos23π8)
1+1=2
m=2

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