Question 236334
Recall that *[Tex \LARGE \sin^2(x)+\cos^2(x)=1]. So *[Tex \LARGE \sin^2(x)=1-\cos^2(x)]. Also, remember that *[Tex \LARGE \csc(x)=\frac{1}{\sin(x)}]



So in this case, *[Tex \LARGE 1-\cos^2(\beta)] becomes *[Tex \LARGE \sin^2(\beta)] and *[Tex \LARGE \csc(\beta)] turns into  *[Tex \LARGE \frac{1}{\sin(\beta)}]



So *[Tex \LARGE \csc(\beta)\left(1-\cos^2(\beta)\right)] simplifies to *[Tex \LARGE \frac{1}{\sin(\beta)}\sin^2(\beta)] which then becomes *[Tex \LARGE \frac{\sin^2(\beta)}{\sin(\beta)}] and finally simplifies to *[Tex \LARG \sin(\beta)]



In the end, *[Tex \LARGE \csc(\beta)\left(1-\cos^2(\beta)\right)=\sin(\beta)]