સમીકરણ sec theta ,, + ,,tan theta , = ,s | vedclass

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

Question

$\sec 	heta+	an 	heta=\sqrt{3}$

$\Rightarrow \quad 1+\sin 	heta=\sqrt{3} \cos 	heta(\cos 	heta 
eq 0)$

$\Rightarrow \quad \sqrt{3} \cos \

Vedclass · Accepted Answer

એક પણ નહી

Vedclass · Answer

$\sec 	heta+	an 	heta=\sqrt{3}$

$\Rightarrow \quad 1+\sin 	heta=\sqrt{3} \cos 	heta(\cos 	heta 
eq 0)$

$\Rightarrow \quad \sqrt{3} \cos 	heta-\sin 	heta=1$

$\Rightarrow \quad \frac{\sqrt{3}}{2} \cos 	heta-\frac{1}{2} \sin 	heta=\frac{1}{2}$

$\Rightarrow \quad \cos 	heta \cos \frac{\pi}{6}-\sin 	heta \sin \frac{\pi}{6}=\cos \frac{\pi}{3}$

$\Rightarrow \quad \cos \left(	heta+\frac{\pi}{6}ight)=\cos \frac{\pi}{3}$

$\Rightarrow \quad 	heta+\frac{\pi}{6}=2 n \pi \pm \frac{\pi}{3}$             $\left( {n \in Z} ight)$

$\Rightarrow \quad 	heta=2 n \pi-\frac{\pi}{6} \pm \frac{\pi}{3}$              $\left( {n \in Z} ight)$

$=2 n \pi+\frac{\pi}{6} 	ext { or } 2 n \pi-\frac{\pi}{2}$

But we reject the values $	heta=2 \mathrm{n} \pi-\frac{\pi}{2}$

$\because \quad \cos 	heta=0$ for this values of $	heta$

$	herefore $ $	heta=2 \mathrm{n} \pi+\frac{\pi}{6}, \mathrm{n} \in \mathrm{I}$

Thus, $	heta=\frac{\pi}{6}$ is the only value of $	heta \in[0,2, \pi]$

સમીકરણ $\sec \theta \,\, + \,\,\tan \theta \, = \,\sqrt 3 \,,\,0\,\, \leqslant \,\,\theta \,\, \leqslant \,\,2\pi$ ના ભિન્ન કેટલા ઉકેલો મળે છે ?

Similar Questions

$-4 \pi \leq x \leq 4 \pi$ માટે $|\cos x|=\sin x$ ના ઉકેલની સંખ્યા મેળવો.

ધારોકે $S=\{\theta \in[0,2 \pi): \tan (\pi \cos \theta)+\tan (\pi \sin \theta)=0\} .$ તો $\sum_{\theta \in s} \sin ^2\left(\theta+\frac{\pi}{4}\right)=...........$.

$\alpha=\sin 36^{\circ}$ એ સમીકરણ $\dots\dots\dots$નું એક બીજ છે.

જો $\cos 3x + \sin \left( {2x - \frac{{7\pi }}{6}} \right) = - 2$, તો $x = . . . . $ (કે જ્યાં $k \in Z$)

જો $\sin 6\theta + \sin 4\theta + \sin 2\theta = 0 $ તો $\theta = $