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

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

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, $A \cap B$

Similar Questions

If $0 \le x \le \pi $ and ${81^{{{\sin }^2}x}} + {81^{{{\cos }^2}x}} = 30$, then $x =$

The equation $3\cos x + 4\sin x = 6$ has

Number of solutions of $8cosx$ = $x$ will be

If $\sin \,\theta + \sqrt 3 \cos \,\theta = 6x - {x^2} - 11,x \in R$ , $0 \le \theta \le 2\pi $ , then the equation has solution for

The solution set of the system of equation

$x\,\, + \,\,y\,\, = \,\,\frac{{2\pi }}{3},\,{\rm{cos}}\,{\rm{x + }}\,{\rm{ cos}}\,{\rm{y}}\,{\rm{ = }}\,\frac{3}{2},$ where $x$ and $y$ are real in