1. Tardigrade
  2. Question
  3. Mathematics
  4. Let A = θ: sin(θ) = tan(θ) and B = θ: cos(θ) = 1 be two sets. Then :

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

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Solution:

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.

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