Question

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

• A. $A=B$
• B. $A\not\subset B$
• C. $B\not\subset A$
• D. $A\subset BandB-A\ne \varphi$

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.
$A\not\subset B.butB\subset A.$