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Prove that....::(Cosecx-Sinx) (Secx-Cosx) (Cotx-Tanx)=1

$L . H . S . = (\cos e c x - \sin x) (\sec x - \cos x) (\cot x - \tan x) = (\frac{1}{\sin x} - \sin x) (\frac{1}{\cos x} - \cos x) (\frac{1}{\tan x} - \tan x) = (\frac{1 - \sin^{2} x}{\sin x}) (\frac{1 - \cos^{2} x}{\cos x}) (\frac{1 - \tan^{2} x}{\tan x}) = (\frac{\cos^{2} x}{\sin x}) (\frac{\sin^{2} x}{\cos x}) (\frac{\sec^{2} x}{\tan x}) = (\frac{\cos^{2} x}{\sin x}) (\frac{\sin^{2} x}{\cos x}) (\frac{1 \times \cos x}{\cos^{2} x \times \sin x}) = 1 = R . H . S . H e n c e p r o v e d .$

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