let f(x)=g(x) / h(x). to get the period of f(x) sometimes in books apply - LCM { period of f(x) & period of h(x) }but sometimes it does nt happen...so what concept pls ... explain in detail.. for ex- period f(x) = cos (sin(6x)) / tan(x/6) is calculated by above concept. but simarly period of sinx/cosx by this concept will be 2 pie but period of tanx is pie.. so i m confused.. pls solve my doubt

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Arun Kumar · Answer

actually sin(x) doesnt have period pi but
sin(x)=mode of (sin(x+pi)
cos(x)= mode of cos(x+pi)
so there are repetition of value but sign are different
and when we divide them sign cancel
so tan(x) is separate than tan(x)
you can consider cos(x) and sin(x) in same category of trigonometric function but tan(x) is different

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