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Question

Prove that tanA+secA-1/tanA-secA+1=1+sinA/cosA

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Solution

tanA + secA -1 / tanA -secA + 1 = (sinA +1-cosA) /(sinA+cosA-1 ) × (sinA+cosA +1)/(sinA+cosA+1)
= (sinA+cosA )(sinA-cosA)+sinA+cosA-cosA+1+sinA-cosA/(sinA+cosA)2-12)
after simplification this is equal to
= 2sinA(1+sin A)/ 2sinA cosA
= (1+sin A)/ cosA
hence right side obtainnd

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