(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 ]
