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JEE Main 201325 AprilOnline
Exam
JEE Main
Year
2013
Date
25 April
Mode
Online
Subject
Mathematics
Chapter
Trigonometric Equations

JEE Main 2013 · 25 April · Online · Mathematics · Trigonometric Equations

Let A=\ θ: (θ)= (θ)\ and B=(θ: (θ)= 1\ be two sets. Then:

Let A={θ:sin⁡(θ)=tan⁡(θ)}\mathrm{A}=\{\theta: \sin (\theta)=\tan (\theta)\} and B=(θ:cos⁡(θ)=\mathrm{B}=(\theta: \cos (\theta)= 1\} be two sets. Then:

Options

  1. AA=B\mathrm{A}=\mathrm{B}
  2. BA⊄BA \not \subset B
  3. CB⊄AB \not \subset A
  4. DA⊂BA \subset B and B−A≠ϕB-A \neq \phi

Correct answer

B. A⊄BA \not \subset B

Step-by-step solution

Let A={θ:sin⁡θ=tan⁡θ}\mathrm{A}=\{\theta: \sin \theta=\tan \theta\} and B={θ:cos⁡θ=1}\mathrm{B}=\{\theta: \cos \theta=1\} Now, A={θ:sin⁡θ=sin⁡θcos⁡θ}A=\left\{\theta: \sin \theta=\frac{\sin \theta}{\cos \theta}\right\} ={θ:sin⁡θ(cos⁡θ−1)=0}=\{\theta: \sin \theta(\cos \theta-1)=0\} ={θ=0,π,2π,3π,……}=\{\theta=0, \pi, 2 \pi, 3 \pi, \ldots \ldots\} For B:cos⁡θ=1⇒θ=π,2π,4π,……\mathrm{B}: \cos \theta=1 \Rightarrow \theta=\pi, 2 \pi, 4 \pi, \ldots \ldots This shows that A\mathrm{A} is not contained in B. i.e. A⊄B\mathrm{A} \not \subset \mathrm{B}. but B⊂A\mathrm{B} \subset \mathrm{A}.
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