PLEASE HELP!!

Verify The Following Identity,
csc x - sin x = cot x cos x

Question

PLEASE HELP!!

Verify The Following Identity,
csc x - sin x = cot x cos x

mathstudent55 · Answer

$ \csc x - \sin x = \cot x \cos x $

(Use the identity csc x= 1/sin x)

$ \dfrac{1}{\sin x} - \sin x = $

(Now we need a common denominator)

$ \dfrac{1}{\sin x} - \sin x \cdot \dfrac{\sin x}{\sin x} = $

$ \dfrac{1}{\sin x} - \dfrac{\sin^2 x}{\sin x} = $

$ \dfrac{1 - \sin^2 x}{\sin x} = $

(Use identity $1 - sin^2 x = cos^2 x$ )

$ \dfrac{\cos^2 x}{\sin x} = $

$ \dfrac{\cos x \cos x}{\sin x} = $

$ \dfrac{\cos x}{\sin x} \cos x = $

$ \cot x \cos x = \cot x \cos x $