Question

how does cos((x+1)pi)/cos(x*pi)=-1?

Answer 1

cos(n*pi) = 1 when n is an even integer

cos(n*pi) = -1 when n is an odd integer

Answer 2

so assuming x is an integer, then if x is odd, then x+1 is even (or vice versa)

Answer 3

if x is odd, then x+1 is even

making cos((x+1)pi) = 1 and cos(x*pi) = -1

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if x is even, then x+1 is odd

making cos((x+1)pi) = -1 and cos(x*pi) = 1

Answer 4

either way, they divide to -1

Answer 5

cos(x+pi)=-cos(x)