How do i prove this identities  1+cosA/1-cosA =1+secA/secA-1

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gsenviro | College Teacher | (Level 1) Educator Emeritus

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Use the identity, cos A = 1/sec A and substitute the value of cos A in the left hand side of the equation:

(1 + cos A)/(1-cos A) = (1+1/sec A)/(1-1/sec A) = [(secA +1)/sec A]/[(secA - 1)/sec A]

cancelling out the sec A from both numerator and denominator, we get

(sec A +1)/(sec A -1) = right hand side. Hence proved.