If sec theta(cos theta+sin theta)=sqrt{2}, th | vedclass

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

Question

(D) Given: $\sec 	heta(\cos 	heta+\sin 	heta)=\sqrt{2}$Since $\sec 	heta = \frac{1}{\cos 	heta}$,we have:$\frac{1}{\cos 	heta}(\cos 	heta+\sin

Vedclass · Accepted Answer

$\sqrt{2}$

Vedclass · Answer

(D) Given: $\sec 	heta(\cos 	heta+\sin 	heta)=\sqrt{2}$Since $\sec 	heta = \frac{1}{\cos 	heta}$,we have:$\frac{1}{\cos 	heta}(\cos 	heta+\sin 	heta)=\sqrt{2}$$1+	an 	heta=\sqrt{2}$$	an 	heta=\sqrt{2}-1$ .....$(1)$Now,we need to find the value of $\frac{2 \sin 	heta}{\cos 	heta-\sin 	heta}$.Dividing the numerator and the denominator by $\cos 	heta$:$\frac{2 	an 	heta}{1-	an 	heta}$Substituting the value of $	an 	heta$ from equation $(1)$:$= \frac{2(\sqrt{2}-1)}{1-(\sqrt{2}-1)}$$= \frac{2(\sqrt{2}-1)}{2-\sqrt{2}}$$= \frac{2(\sqrt{2}-1)}{\sqrt{2}(\sqrt{2}-1)}$$= \frac{2}{\sqrt{2}} = \sqrt{2}$

If $\sec \theta(\cos \theta+\sin \theta)=\sqrt{2},$ then what is the value of $\frac{2 \sin \theta}{\cos \theta-\sin \theta} ?$

Similar Questions

$\cos \frac{\pi }{5} \cos \frac{2\pi }{5} \cos \frac{4\pi }{5} \cos \frac{8\pi }{5} = $

$\sin 4\theta$ can be written as

If $\sqrt{2} \tan 2 \theta = \sqrt{6}$ and $0^{\circ} < \theta < 45^{\circ},$ then the value of $\sin \theta + \sqrt{3} \cos \theta - 2 \tan^{2} \theta$ is

If $\sin 5 \theta = \cos 20^{\circ}$ where $0^{\circ} < \theta < 90^{\circ}$,then the value of $\theta$ is (in degrees):

If $\cos \theta = \frac{3}{5}$ and $\cos \phi = \frac{4}{5},$ where $\theta$ and $\phi$ are positive acute angles,then $\cos \frac{\theta - \phi}{2} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module