Question

prove that sin4(π\8)+sin4(3π\8) +sin4 (5π/4) +sin4(7π\8) =3/2​

Answer 1

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Answer 2

Answer:

sin 4 8π + sin 4 3 8π + sin 4 5 8π + sin 4 7 8π sin5 8π = cos 2π − 8 5π = cos 8 3π

similarly,

sin 8 7π = cos 8π sin 4 8π + cos 4 8π + sin 4 3 8π + cos 4 3 8π = (sin 2 8π + cos 2 8π ) 2 + (sin 2 3 8π + cos 2 3 8π ) 2−2sin 2 8π cos 2 8π − sin 2 3 8π cos 2 3 8π sin 2 8π + cos 2 8π = 21 .4sin 2 8π cos 2 8π = 21 (2sin 8π cos 8π ) 2 = 21 sin 2 4π samefor2sin

2 3 8π cos 2 3 8π

So,

(sin 2 8π + cos 2 8π ) 2 +(sin

2 3 8π +cos 2 3 8π ) 2 −2s28π cos 28π − sin 2 3 8π cos 2 3 8π = 1 + 1− 21 sin 24π − 21 sin 2 3 4π =2− 21 ( 21 + 21 )=2− 21 = 23