All possible values of theta in[0,2 pi] for w | vedclass

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

Question

$\sin 2 	heta+	an 2 	heta>0$

$\Rightarrow \sin 2 	heta+\frac{\sin 2 	heta}{\cos 2 	heta}>0$

$\Rightarrow \sin 2 	heta \frac{(\cos 2

Vedclass · Accepted Answer

$\left(0, \frac{\pi}{4}\right) \cup\left(\frac{\pi}{2}, \frac{3 \pi}{4}\right) \cup\left(\pi, \frac{5 \pi}{4}\right) \cup\left(\frac{3 \pi}{2}, \frac{7 \pi}{4}\right)$

Vedclass · Answer

$\sin 2 	heta+	an 2 	heta>0$

$\Rightarrow \sin 2 	heta+\frac{\sin 2 	heta}{\cos 2 	heta}>0$

$\Rightarrow \sin 2 	heta \frac{(\cos 2 	heta+1)}{\cos 2 	heta}>0 \Rightarrow 	an 2 	heta\left(2 \cos ^{2} 	hetaight)>0$

Note : $\cos 2 	heta 
eq 0$

$\Rightarrow 1-2 \sin ^{2} 	heta 
eq 0 \Rightarrow \sin 	heta 
eq \pm \frac{1}{\sqrt{2}}$

Now, $	an 2 	heta(1+\cos 2 	heta)>0$

$\Rightarrow 	an 2 	heta>0 \quad($ as $\cos 2 	heta+1>0)$

$\Rightarrow 2 	heta \in\left(0, \frac{\pi}{2}ight) \cup\left(\pi, \frac{3 \pi}{2}ight) \cup\left(2 \pi, \frac{5 \pi}{2}ight) \cup\left(3 \pi, \frac{7 \pi}{2}ight)$

$\Rightarrow 	heta \in\left(0, \frac{\pi}{4}ight) \cup\left(\frac{\pi}{2}, \frac{3 \pi}{4}ight) \cup\left(\pi, \frac{5 \pi}{4}ight) \cup\left(\frac{3 \pi}{2}, \frac{7 \pi}{4}ight)$

As $\sin 	heta 
eq \pm \frac{1}{\sqrt{2}} ;$ which has been already considered

All possible values of $\theta \in[0,2 \pi]$ for which $\sin 2 \theta+\tan 2 \theta>0$ lie in

Similar Questions

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

The number of solutions of the equation $\cos \left(x+\frac{\pi}{3}\right) \cos \left(\frac{\pi}{3}-x\right)=\frac{1}{4} \cos ^{2} 2 x, x \in[-3 \pi$ $3 \pi]$ is

If $A, B, C, D$ are the angles of a cyclic quadrilateral taken in order, then
$cos(180^o + A) + cos(180^o -B) + cos(180^o -C) -sin(90^o -D)=$

If $\alpha ,\,\beta ,\,\gamma $ and $\delta $ are the solutions of the equation $\tan \left( {\theta + \frac{\pi }{4}} \right) = 3\,\tan \,3\theta $ , no two of which have equal tangents, then the value of $tan\, \alpha + tan\, \beta + tan\, \gamma + tan\, \delta $ is

Find the general solution of the equation $\sin x+\sin 3 x+\sin 5 x=0$