((tana+seca-1)/(tana-seca+1))^2
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Step-by-step explanation:
Formula - sec^2A = 1 + tan^2A
sec^2 - tan^2A = 1
{(tanA + secA - 1) / (tanA - secA + 1)}^2
substitute that 1
[{(tanA + secA - (sec^2A - tan^2A)} / (tanA - secA + 1)]^2
[{(tanA + secA) - (secA + tanA)(secA - tanA)} / (tanA - secA + 1)]^2
take - tanA + secA common
= [(tanA + secA) {1 - (secA - tanA)} / (tanA - secA + 1)]^2
= {tanA + secA(1 - secA + tanA) / tanA - secA + 1}^2
= (tanA + secA)^2
= (sinA/cosA + 1/cosA)^2
= (1+ sinA)^2 / cos^2A
cos^2A = 1 - sin^2A
= (1 + sin^A)^2 / 1 - sin^2A
= (1+ sinA)^2 / (1 - sinA)(1 + sinA)
= (1 + sinA) / (1 - sinA)
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