Question

Csc B - sin B = cot B cos B

Answer 1

Explanation:

`\csc\beta-\sin\beta=\cot\beta\cos\beta\\\\\text{Use}\ \csc x=(1)/(\sin x)\\\\L_S=(1)/(\sin\beta)-\sin\beta=(1)/(\sin\beta)-(\sin^2\beta)/(\sin\beta)=(1-\sin^2\beta)/(\sin\beta)\\\\\\\text{Use}\ \sin^2x+\cos^2x=1\to\cos^2x=1-\sin^2x\\\\L_S=(\cos^2\beta)/(\sin\beta)}=(\cos\beta\cdot\cos\beta)/(\sin\beta)=(\cos\beta)/(\sin\beta)\cdot\cos\beta\\\\\\\text{Use}\ \cot x=(\cos x)/(\sin x)\\\\L_S=\cot\beta\cos\beta\\\\R_S=\cot\beta\cos\beta\\\\L_S=R_S`