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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Trigonometric Equations

NTA Abhyas 2020 · Mathematics · Trigonometric Equations

If (α + β) =0, then (α + +2β)is equal to

If cot⁡(α+β)=0,\cot \left(\alpha + \beta\right) =0, then \sin \left(\alpha ++2\beta\right)is equal to

Options

  1. Asinαsin \alpha
  2. Bcosαcos \alpha
  3. Csinβsin \beta
  4. Dcos⁡2β\cos 2\beta

Correct answer

A. sinαsin \alpha

Step-by-step solution

Given, cot⁡(α+β)=0⇒cos⁡(α+β)=0\cot \left(\alpha + \beta\right) = 0 ⇒ \cos \left(\alpha + \beta\right) = 0

⇒α+β=(2n+1)π2,n∈I⇒ \alpha + \beta = \left(2n + 1\right)\dfrac{\pi}{2}, n \in I

∴ \sin \left(\alpha ++2\beta\right) =sin$lleft(2α++2β−α)sin \$lleft(2\alpha ++2\beta - \alpha)

=sin[(2n+1)π−α]<br/><br/>= sin [ \left(2n + 1\right)\pi - \alpha ]<br/><br/>= \sin (2n\pi + \pi - \alpha )

=sin⁡(π−α)=sinα= \sin \left(\pi - \alpha\right) = sin \alpha
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