Prove the following: cosec(90°-x) sin (180°-x) cot(360°-x)/ sec(180°+x) tan(90°+x) sin(-x)=1

Question

Prove the following: 

\(\frac {cosec(90°-x)\, sin(180°-x)\, cot(360°-x)}{sec(180°+x)\, tan(90°+x)\,sin(-x)} = 1\)

cosec(90°-x) sin (180°-x) cot(360°-x)/ sec(180°+x) tan(90°+x) sin(-x)=1

Answer 1

L.H.S = \(\frac {cosec(90°-x)\, .sin(180°-x)\, .cot(360°-x)}{sec(180°+x)\, .tan(90°+x)\,.sin(-x)}\)

         = \(\frac{sec\,x\,sin\,x(-cot\,x)}{-sec\,x).(-cot\,x).(-sin\,x)}\)

= 1

= R.H.S