sin^4 ⁡ 8+ cos^4 ⁡ 3 8- sin^4 ⁡ 3 8+ sin^4 5 8+ cos^4 ⁡ 7 8- sin^4 ⁡ 7 8=

Question

Accepted Answer

Correct answer: D. (d) Given that, sin^4 ⁡ 8+ cos^4 ⁡ 3 8- sin^4 ⁡ 3 8+ sin^4 ⁡ 5 8+ cos^4 ⁡ 7 8- sin^4 ⁡ 7 8 = sin^4 ⁡ 8+ cos^4 ⁡ 3 8- sin^4 ⁡ 3 8+ sin^4 ⁡( - 3 8) + cos^4 ⁡ 7 8- sin^4 ⁡( - 8) = sin^4 ⁡ 8+ cos^4 ⁡ 3 8- sin^4 ⁡ 3 8+ sin^4 ⁡ 3 8+ cos^4 ⁡ 7 8- sin^4 ⁡ 8 = cos^4 ⁡ 3 8+ cos^4 ⁡ 7 8= cos^4 ⁡ 3 8+ cos^4 ⁡( - 8) = cos^4 ⁡ 3 8+(- cos ⁡ 8)^4= cos^4 ⁡ 3 8+ cos^4 ⁡ 8 = ( cos^2 ⁡ 3 8 )^2+ ( cos^2 ⁡ 8 )^2= ( 1+ cos ⁡ 3 42 )^2+ ( 1+ cos ⁡ 42 )^2 = 14((1- 1 2)^2+(1+ 1 2)^2) = 14(1+ 12- 2 2+1+ 12+ 2 2)= 34

$sin^{4} \frac{π}{8} + cos^{4} \frac{3 π}{8} - sin^{4} \frac{3 π}{8} + sin^{4} \frac{5 π}{8} + cos^{4} \frac{7 π}{8} - sin^{4} \frac{7 π}{8} =$

Solution

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