prove that: cotA-cosA/ cotA +cosA = cosecA-1/cosecA+1

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Solution

(cotA -cosA)/(cotA + cosA) = (cosecA-1)/(cosecA+1)

(cotA -cosA)/(cotA + cosA)
((cosA/sinA)-cosA)/((cosA/sinA)-cosA) cotA=cosA/sinA
taking cosA common from numretor nd denominatr nd cancelling it we get

((1/sinA)-1)/((1/sinA)+1) since 1/sinA=cosecA
therfore
(cosecA-1)/(cosecA+1).

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\frac{c o t A + c o s e c A - 1}{c o t A - c o s e c A + 1} = \frac{1 + c o s A}{s i n A}

\frac{c o t A + c o s e c A - 1}{c o t A - c o s e c A + 1} = \frac{1 + c o s A}{s i n A} = c o s e c θ + c o t θ = \frac{s i n A}{1 - c o s A}

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