Let A = left{ {theta ,:,sin ,left( theta | vedclass

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Question

Let $A = \left\{ {	heta \,:\,\sin \, 	heta = 	an \,	heta } ight\}$

and $B = \left\{ {	heta \,:\,\cos \, 	heta   = 1} ight\

Vedclass · Accepted Answer

$A 
ot\subset B$

Vedclass · Answer

Let $A = \left\{ {	heta \,:\,\sin \, 	heta = 	an \,	heta } ight\}$

and $B = \left\{ {	heta \,:\,\cos \, 	heta   = 1} ight\}$

Now, $A\, = \,\left\{ {	heta \,\,:\,\,\sin \,\,	heta \, = \,\frac{{\sin \,	heta }}{{\cos \,	heta }}} ight\}$

$ = \,\{ 	heta \,:\,\sin \,	heta \,\,(\cos \,	heta \,\, - \,1)\, = \,0\} $

$ = \,\{ 	heta \, = \,0\,,\,\pi \,,\,2\pi \,,\,3\pi ,\,.....\} $

For $B{\mkern 1mu} \,:\,\cos \,	heta \, = \,1\,\, \Rightarrow \,	heta \, = \,\pi \,,\,2\pi \,,\,4\pi \,,.....{\mkern 1mu} $

This showns that $A$ is not contained in $B$ i.e. 

$A\, 
ot\subset \,B$ but $B\, \subset \,A$.

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

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