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  • Prove the following identity: (sec x -1)^2 - (tan x - sin x)^2 = (1 - cos x)^2

Prove the following identity: (sec x -1)^2 - (tan x - sin x)^2 = (1 - cos x)^2

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L.H.S. \\ (\sec x -1)^2 - (\tan x - \sin x)^2 = ( \frac{1}{\cos x} - 1)^2-(\frac{\sin x}{\cos x}- \sin x)^2\\ = ( \frac{1}{\cos x} - 1)^2(1-\sin^2 x)\\ =\frac{(1-\cos x)^2 }{\cos^2 x} \cos^2x =(1-\cos x)^2

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Ravindra Pindel

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