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Question
If sec A + tan A = p, show that:
`sin A = (p^2 - 1)/(p^2 + 1)`
Solution
`(p^2 - 1)/(p^2 + 1)`
= `((secA + tanA)^2 - 1)/((secA + tanA)^2 + 1)`
= `(sec^2A + tan^2A + 2tanA secA - 1)/(sec^2A + tan^2A + 2tanA secA + 1)`
= `(tan^2A + tan^2A + 2tanA secA)/(sec^2A + sec^2A + 2tanA secA)`
= `(2tan^2A + 2tanA secA)/(2sec^2A + 2tanA secA)`
= `(2tanA(tanA + secA))/(2secA(tanA + secA)`
= sin A
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