Step-by-step explanation:
[tex]\csc\beta-\sin\beta=\cot\beta\cos\beta\\\\\text{Use}\ \csc x=\dfrac{1}{\sin x}\\\\L_S=\dfrac{1}{\sin\beta}-\sin\beta=\dfrac{1}{\sin\beta}-\dfrac{\sin^2\beta}{\sin\beta}=\dfrac{1-\sin^2\beta}{\sin\beta}\\\\\\\text{Use}\ \sin^2x+\cos^2x=1\to\cos^2x=1-\sin^2x\\\\L_S=\dfrac{\cos^2\beta}{\sin\beta}}=\dfrac{\cos\beta\cdot\cos\beta}{\sin\beta}=\dfrac{\cos\beta}{\sin\beta}\cdot\cos\beta\\\\\\\text{Use}\ \cot x=\dfrac{\cos x}{\sin x}\\\\L_S=\cot\beta\cos\beta\\\\R_S=\cot\beta\cos\beta\\\\L_S=R_S[/tex]
