Question

cosec theta(1+cos theta)(cosec - cot theta ) = 1

Answer 1

here's your answer :-

cosec ​θ( 1 + cosθ ) ( cosecθ - cotθ ) = 1

L.H.S = cosecθ ( cosecθ - cotθ + cosθcosecθ - cosθcotθ )
         = cosecθ ( cosecθ - cotθ + cosθ/sinθ - cosθcotθ )        [ cosecθ = 1/sinθ ]
         = cosecθ ( cosecθ - cotθ​ + cotθ - cosθ​cotθ​ )
         = cosecθ ( cosecθ - cosθcotθ )
         = cosec2θ - cosecθ . cotθ . cosθ )
         = cosec2θ - 1/sinθ . cosθ/sinθ .cosθ
         = cosec2θ - cos2θ/sin2θ                        [ Identity -> cosec2θ - cot2θ = 1 ]
​         = cosec2θ - cot2θ
         = 1
L.H.S = R.H.S 
 
hope it helps u ;)
mark as brainliest answer ;)