Question

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

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

Answer 1

Answer: (B)

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