prove the following identity: 1+cos A/1-cos A=tan^2A/(sec A-1)^2
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Step-by-step explanation:
RHS = tan^2A/(secA-1)^2
= sec^2A-1/(secA-1)^2
= (secA-1)(secA+1)/ (secA-1)(secA-1)
= (secA + 1)/(secA-1)
= [ 1/cosA +1] ÷ [1/cosA-1]
= [1/cosA + cosA/cosA] ÷[1/cosA - cosA/cosA]
= (1+ cosA)/(1-cosA)
= LHS
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