Question

PLEASE HELP!!

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

Answer 1

\( \csc x - \sin x = \cot x \cos x \)

(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 \(1 - sin^2 x = cos^2 x\) )

\( \dfrac{\cos^2 x}{\sin x} = \)

\( \dfrac{\cos x \cos x}{\sin x} = \)

\( \dfrac{\cos x}{\sin x} \cos x = \)

\( \cot x \cos x = \cot x \cos x \)