Solve the equation cos^n x − sin^n x = 1, where n is a natural number.
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Step-by-step explanation:
For 0<x<2π and positive even n, the only solution for cosnx−sinnx=1 is π.
The argument is simple as 0≤cos^nx,sin^nx≤1.
Hence, cos^nx−sin^nx=1 iff cos^nx=1 and sin^nx=0.
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