sec A -1 ÷ sec A+1 =(cot A-cosec A)^2
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rhs = (cotA- cosecA)^2
= [cosA/sinA -1/sinA]^2
=[(cosA-1)/sinA]^2
=(cosA-1)^2/sin^2A
=(1-cosA)^2/[1- cos^2A]
=[(1-cosA)(1-cosA)]/[(1+cosA)(1-cosA)]
=(1-cosA)/(1+cosA)
divide numerator and denominator with cosA
=[1/cosA - cosA/cosA]/[1/cosA + cosA/cosA]
=[1/cosA -1]/[1/cosA +1]
=(secA -1)/(secA +1)
=lhs
= [cosA/sinA -1/sinA]^2
=[(cosA-1)/sinA]^2
=(cosA-1)^2/sin^2A
=(1-cosA)^2/[1- cos^2A]
=[(1-cosA)(1-cosA)]/[(1+cosA)(1-cosA)]
=(1-cosA)/(1+cosA)
divide numerator and denominator with cosA
=[1/cosA - cosA/cosA]/[1/cosA + cosA/cosA]
=[1/cosA -1]/[1/cosA +1]
=(secA -1)/(secA +1)
=lhs
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