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Question
If secθ + tanθ = m , secθ - tanθ = n , prove that mn = 1
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Solution
LHS = mn = (secθ + tanθ) (secθ - tanθ)
⇒ LHS = `sec^2θ - tan^2θ` [Because (a-b)(a+b) = a2 - b2]
⇒ LHS = 1 [Since `1 + tan^2θ = sec^2θ`]
Hence , mn = 1
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