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Different periodicity for equivalent equations in W|A?

Posted 8 months ago
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Hello,

I was investigating the equation sin(sin(x))/sin(2sin(x)) in my work. When I type it on Wolfram|Alpha, it says the periodicity is 2π and the result is 'csc(2 sin(x)) sin(sin(x))', whose periodicity is also 2π.

However, Wolfram|Alpha also says such equations are equivalent to '1/(2*cos(sin(x)))' (also represented as 'sec(sin(x))/2)'). When I type these equations on Wolfram|Alpha, it says the periodicity is only π.

It's very strange. When I type 'csc(2 sin(x)) sin(sin(x)) - sec(sin(x))/2)', the result is 0 (indicating they are the same equation), but they present different periodicity according to the same website.

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