Let A=left{theta in R mid cos ^2(sin theta)+s | vedclass

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Question

(a)

We have,

$A=\left\{	heta \in R \mid \cos ^2(\sin 	heta)+\sin ^2(\cos 	heta)=1ight\}$

$	herefore \cos ^2(\sin 	heta)+\sin ^2(\cos \

Vedclass · Accepted Answer

is the empty set

Vedclass · Answer

(a)

We have,

$A=\left\{	heta \in R \mid \cos ^2(\sin 	heta)+\sin ^2(\cos 	heta)=1ight\}$

$	herefore \cos ^2(\sin 	heta)+\sin ^2(\cos 	heta)=1$

$	herefore \quad \sin 	heta=\cos 	heta \Rightarrow 	an 	heta=1$

$\Rightarrow \quad 	heta=n \pi+\frac{\pi}{4}$

$\quad B=\{	heta \in R \mid \cos (\sin 	heta) \sin (\cos 	heta)=0$

$\quad \cos (\sin 	heta) \sin (\cos 	heta)=0$

$\quad \cos (\sin 	heta)=0 	ext { or } \sin (\cos 	heta)=0$

$\quad \sin 	heta=(2 n+1) \frac{\pi}{2} 	ext { or } \cos 	heta=2 n \pi$

$	herefore 	ext { Clearly } A \cap B=0$

$	herefore A \cap B 	ext { is an empty set. }$

Let $A=\left\{\theta \in R \mid \cos ^2(\sin \theta)+\sin ^2(\cos \theta)=1\right\}$ and $B=\{\theta \in R \mid \cos (\sin \theta) \sin (\cos \theta)=0\}$. Then, $A \cap B$

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