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If tanθ = 12 and tanΦ = 13, then the value of θ + Φ is ______.

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Question

If tanθ = `1/2` and tanΦ = `1/3`, then the value of θ + Φ is ______.

Options

  • `pi/6`

  • `pi`

  • 0

  • `pi/4`

MCQ
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Solution

If tanθ = `1/2` and tanΦ = `1/3`, then the value of θ + Φ is `bbunderline(pi/4)`.

Explanation:

tanθ = `1/2` and tanΦ = `1/3`

We know that,

tan(θ + Φ) = `(tantheta + tanphi)/(1 - tantheta tanphi)`

= `(1/2 + 1/3)/(1 - 1/2 xx 1/3)`

= `(5/6)/(5/6)` 

= 1

⇒ tan(θ + Φ) = `tan pi/4`

⇒ θ + Φ = `pi/4`

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Values of Trigonometric Functions at Multiples and Submultiples of an Angle
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Chapter 3: Trigonometric Functions - Exercise [Page 55]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 11
Chapter 3 Trigonometric Functions
Exercise | Q 32 | Page 55

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