Cos²(π/10)+Cos²(2π/5)+Cos²(3π/5)+Cos²(9π/10)=2​

Question

Cos²(π/10)+Cos²(2π/5)+Cos²(3π/5)+Cos²(9π/10)=2​

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Evelyn 3 weeks 2021-09-10T01:00:35+00:00 2 Answers 0 views 0

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    2021-09-10T01:01:36+00:00

    Answer:

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    2021-09-10T01:01:42+00:00

    Answer:

    cos²180°/16+cos²540°/16+cos²900°/16+cos²1260°/16

    =cos²π/16+cos²3π/16+cos²5π/16+cos²7π/16 [180°/16=π/16 (say)]

    =cos²π/16+cos²3π/16+cos²(π/2-3π/16)+cos²(π/2-π/16)

    =cos²π/16+cos²3π/16+sin²3π/16+sin²π/16 [∵. cos(π/2-Ф)=sinФ]

    =(sin²π/16+cos²π/16)+(sin²3π/16+cos²3π/16)

    =1+1 [∵, sin²Ф+cos²Ф=1]

    =2

    Step-by-step explanation:

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