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If α + β = π4, then the value of (1 + tan α)(1 + tan β) is ______. - Mathematics

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Question

If α + β = `pi/4`, then the value of (1 + tan α)(1 + tan β) is ______.

Options

  • 1

  • 2

  • –2

  • Not defined

MCQ
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Solution

If α + β = `pi/4`, then the value of (1 + tanα)(1 + tanβ) is 2.

Explanation:

Given that: α + β = `pi/4`

⇒ `(tanalpha + tanbeta)/(1 - tanalpha tanbeta)` = 1

⇒ tanα + tanβ = 1 – tanα tanβ

⇒ tanα + tanβ + tanα tanβ = 1

⇒ 1 + tanα + tanβ + tanα tanβ = 1 + 1

⇒ 1(1 + tanα) + tanβ(1 + tanα) = 2

⇒ (1 + tanα)(1 + tanβ) = 2

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Chapter 3: Trigonometric Functions - Exercise [Page 58]

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NCERT Exemplar Mathematics [English] Class 11
Chapter 3 Trigonometric Functions
Exercise | Q 51 | Page 58

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