Question

Let $A = \left\{\theta: sin \left(\theta\right)=tan\left(\theta\right) and \,B=(\theta: cos \left(\theta\right)=1\right\}\quad$ be two sets. Then :

• A. $A=B$
• B. $A ⊄ B$
• C. $B ⊄A$
• D. $A \subset B \, and \, B-A \ne\phi$

Answer 1

Answer: (B)

Let $A$ = {$\theta$: sin $\theta$ = tan $\theta$}
and $B$ = {$\theta$: cos$\theta$= 1}
Now, $A$ = $\left\{\theta:sin \, \theta=\frac{sin\, \theta}{cos \, \theta}\right\}$
= {$\theta$: sin $\theta$ (cos $\theta$ -1) = 0}
= {$\theta$=0, $\pi$,2$\pi$3$\pi$.....}
For $B$ : $cos \theta = 1$ $\Rightarrow \theta=\pi, 2\pi, 4\pi,$.......
This shows that $A$ is not contained in $B$. i.e.
$A ⊄ B. \, but \, B\subset A.\quad$