Cos^2π/8+cos^23π/8+cos^25π/8+cos^27π/8
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) The statement is not full; it is truncated; this may be reason that each part is not separated but continuous. Assuming it involves 4 parts, it should be:
cos²(π/8) + cos²(3π/8) + cos²(5π/8) + cos²(7π/8)
ii) Applying cos²θ = {1 + cos(2θ)}/2, the above one is
= {1 + cos(π/4)}/2 + {1 + cos(3π/4)}/2 + {1 + cos(5π/4)}/2 + {1 + cos(7π/4)}/2
iii) Grouping them, it is =
(1/2 + 1/2 + 1/2 + 1/2) + (1/2)[{cos(π/4) + cos(3π/4)} + {cos(5π/4) + cos(7π/4)}]
= 2 + (1/2)[0 + 0] = 2
cos²(π/8) + cos²(3π/8) + cos²(5π/8) + cos²(7π/8)
ii) Applying cos²θ = {1 + cos(2θ)}/2, the above one is
= {1 + cos(π/4)}/2 + {1 + cos(3π/4)}/2 + {1 + cos(5π/4)}/2 + {1 + cos(7π/4)}/2
iii) Grouping them, it is =
(1/2 + 1/2 + 1/2 + 1/2) + (1/2)[{cos(π/4) + cos(3π/4)} + {cos(5π/4) + cos(7π/4)}]
= 2 + (1/2)[0 + 0] = 2
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