If cos⁡17x=f(cos⁡x), then show that sin⁡17x=f(sin⁡x)

Terrie Lang

Terrie Lang

Answered

2022-01-16

If cos17x=f(cosx), then show that sin17x=f(sinx)

Answer & Explanation

Elois Puryear

Elois Puryear

Expert

2022-01-17Added 30 answers

cos17x=f(cosx)
cos17(π2x)=f(cos(π2x))
cos(17π217x)=f(sinx)
cos(8π+π217x)=f(sinx)
cos(π217x)=f(sinx)
sin17x=f(sinx)
The generalisation is that cosnx=f(cosx)sinnx=f(sinx) holds for all n=4k+1,kZ

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