Question

(Cosec theta -sec theta)(cot theta -tan theta)= (cosec theta +sec theta )(sec theta .cosec theta -2)

Answer 1

its improper question write the proper question

Answer 2

there is problem in ur question

THIS IS THE RYT ONE

To prove,

(cosec θ - sin θ)(sec θ - cos θ)(tan θ + cot θ)=1

Proof:

LHS =(1/sin θ - sin θ)(1/cos θ - cos θ)(tan θ+1/tan θ)

         =(1-sin²θ)/sinθ (1-cos²θ)/cosθ(1+tan²θ)/tanθ

         =(cos²θ)/sinθ (sin²θ)/cosθ sec²θ/tanθ

         =cos θ sin θ (1/cos²θ)/(sinθ/cosθ)

         =cos θ sin θ(1/cos²θ)(cosθ/sinθ)

         =cos θ sin θ (cos θ/sin θ cos²θ)

         =cos θ sin θ (1/sin θ cos θ)

         =cos θ sin θ/sin θ cos θ

         =1=RHS

            ∴ Hence proved

                  Hope it Helps!!