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determine whether sec x -tanxsinx=cosx is a possible identity

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loneguy

[tex]\text{L.H.S}\\\\\sec x - \tan x \sin x\\\\\\=\dfrac{1}{\cos x}- \dfrac{\sin x }{ \cos x } \cdot \sin x\\\\\\=\dfrac 1{\cos x} - \dfrac{\sin^2 x}{\cos x}\\\\\\=\dfrac{1- \sin^2 x}{\cos x}\\\\\\=\dfrac{\cos^2 x}{\cos x}~~~~~~~~~~~~~;[\sin^2 x + \cos^2 x = 1]\\\\\\=\cos x\\\\\\=\text{R.H.S}\\\\\text{Since both sides are equal, the given equation is an identity.}[/tex]

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