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Grade 11Trigonometry

2 sin^4(pi/8)+2 sin^4(3pi/8)=3/2 how?

Profile image of sarthak
11 Years agoGrade 11
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1 Answer

Profile image of Y RAJYALAKSHMI
ApprovedApproved Tutor Answer11 Years ago
2sin4(pi/8) + sin4(3pi/8) = 2sin4(pi/8) + 2sin4((pi/2) – pi/8))
= 2sin4(pi/8) + 2cos4(pi/8) = 2( sin4(pi/8) + cos4(pi/8))   (add & subtract 2sin2(pi/8)cos2(pi/8))
= 2[(sin2(pi/8) + cos2(pi/8))2 – 2sin2(pi/8)cos2(pi/8))]
= 2[1 – 2sin2(pi/8)cos2(pi/8)] = 2 – 4 sin2(pi/8) cos2(pi/8) = 2 – sin2(pi/4)
= 2 – ½ = 3/2
 

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