Respuesta :

(secθ ÷ (cscθ - cotθ)) - (secθ ÷ (cscθ + cotθ)) = 2cscθ

LHS [ Left Hand Side ]

= (secθ ÷ (cscθ - cotθ)) - (secθ ÷ (cscθ + cotθ))

= [(secθ(cscθ+ cotθ)) - (secθ(cscθ - cotθ))] ÷ [(cscθ - cotθ)(cscθ + cotθ)] 
            [ Simplifying over a single denominator ]

= [(secθ)(cscθ+ cotθ - (cscθ - cotθ)] ÷ [csc²θ - cot²θ]
            [ Taking secθ common and more further simplification ]

= [(secθ)(cscθ+ cotθ - cscθ + cotθ)] ÷ [csc²θ - cot²θ]

= [(secθ)(2cotθ)] ÷ [1]    [cot²θ + 1= csc²θ]

= (secθ)(2cotθ)

= (1÷cosθ)(2*(cosθ ÷ sinθ)  [secθ = 1÷cosθ and cotθ = cosθ ÷ sinθ]

= 2*(1÷sinθ)

= 2cscθ [cscθ = 1÷sinθ]

= RHS   [ Right Hand Side ]

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