Let A = { theta : sin(theta) = tan(theta) } a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) For set $A$,we have $\sin(	heta) = 	an(	heta)$.This implies $\sin(	heta) = \frac{\sin(	heta)}{\cos(	heta)}$,which gives $\sin(	heta)(1 - \f

Vedclass · Accepted Answer

$A 
ot\subset B$

Vedclass · Answer

(B) For set $A$,we have $\sin(	heta) = 	an(	heta)$.This implies $\sin(	heta) = \frac{\sin(	heta)}{\cos(	heta)}$,which gives $\sin(	heta)(1 - \frac{1}{\cos(	heta)}) = 0$.Thus,$\sin(	heta) = 0$ or $\cos(	heta) = 1$.If $\sin(	heta) = 0$,then $	heta = n\pi$ for $n \in \mathbb{Z}$.If $\cos(	heta) = 1$,then $	heta = 2n\pi$ for $n \in \mathbb{Z}$.Combining these,$A = \{ n\pi : n \in \mathbb{Z} \} = \{ 0, \pm\pi, \pm 2\pi, \dots \}$.For set $B$,we have $\cos(	heta) = 1$,which implies $	heta = 2n\pi$ for $n \in \mathbb{Z}$.Thus,$B = \{ 2n\pi : n \in \mathbb{Z} \} = \{ 0, \pm 2\pi, \pm 4\pi, \dots \}$.Comparing the two sets,every element of $B$ is in $A$,so $B \subset A$.However,$\pi \in A$ but $\pi 
otin B$,so $A 
ot\subset B$.

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

Similar Questions

Let $x_{1}, x_{2}, \ldots, x_{15}$ be $15$ distinct numbers chosen from $1, 2, 3, \ldots, 15$. Then,the value of $(x_{1}-1)(x_{2}-1)(x_{3}-1) \ldots (x_{15}-1)$ is

If $A$ and $B$ are two sets,then $A \cup (A \cap B)$ is equal to

Write the set $\{ \frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \frac{5}{6}, \frac{6}{7} \}$ in the set-builder form.

List all the elements of the following set:
$C = \{ x : x \text{ is an integer; } x^2 \le 4 \}$

Given the sets $A = \{1, 3, 5\}$,$B = \{2, 4, 6\}$,and $C = \{0, 2, 4, 6, 8\}$,which of the following sets can be considered as a universal set for all three sets $A$,$B$,and $C$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module