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

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

Grade:11

1 Answers

Y RAJYALAKSHMI
45 Points
9 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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