Question

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Answer 1

Answer:

Step-by-step explanation:

cosФ=1/2(a+1/a)

cos2Ф=1/2(a²+1/a²)

cos2Ф=2cos²Ф-1

          =2(1/2(a+1/a))²-1

          =2×1/4(a+1/a)²-1

          =1/2(a+1/a)²-1

          =  1/2(a²+1/a²+2a×1/a)-1

          =1/2(a²+1/a²+2)-1

          =1/2(a²+1/a²)+1/2×2-1

          =1/2(a²+1/a²)+1-1

cos2Ф  =1/2(a²+1/a²)

hence proved

cos3Ф=4cos³Ф-3cosФ

          =4(1/2(a+1/a))³-3(1/2 (a+1/a))

           =4×1/8(a+1/a)³-3/2(a+1/a)

            =1/2(a³+1/a³+3a²×1/a+3a×1/a²)-3/2(a+1/a)

             =1/2(a³+1/a³+3a+3/a)-3a/2-3/2a

             =1/2(a³+1/a³)+3a/2 +3/2a-3a/2 -3/2a

  cos3Ф   =1/2(a³+1/a³)

hence proved