If Secθ + Tanθ = M , Secθ - Tanθ = N , Prove that Mn = 1 - Mathematics

Question

If secθ + tanθ = m , secθ - tanθ = n , prove that mn = 1

Sum

Solution

LHS = mn = (secθ + tanθ) (secθ - tanθ)

⇒ LHS = $\sec^{2} θ - \tan^{2} θ$ [Because (a-b)(a+b) = a² - b²]

⇒ LHS = 1 [Since $1 + \tan^{2} θ = \sec^{2} θ$ ]

Hence , mn = 1

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Trigonometric Identities

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Chapter 21: Trigonometric Identities - Exercise 21.2

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Chapter 21 Trigonometric Identities
Exercise 21.2 | Q 6

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If Secθ + Tanθ = M , Secθ - Tanθ = N , Prove that Mn = 1 - Mathematics

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