Question

prove the following identity: 1+cos A/1-cos A=tan^2A/(sec A-1)^2​

Answer 1

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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