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

If $\sec \alpha + \tan \alpha = 2,$ then the value of $\sin \alpha$ is (assume that $0 < \alpha < 90^{\circ}$).

If $\sin \theta + \sin^2 \theta = 1$,then $\cos^2 \theta + \cos^4 \theta$ is equal to

The value of $\frac{\tan 40^{\circ}+\tan 20^{\circ}}{1-\cot 70^{\circ} \cot 50^{\circ}}$ is equal to

The expression $2\cos \frac{\pi }{13} \cos \frac{9\pi }{13} + \cos \frac{3\pi }{13} + \cos \frac{5\pi }{13}$ is equal to

If $x = \operatorname{cosec} \theta - \sin \theta$ and $y = \sec \theta - \cos \theta$,then the relation between $x$ and $y$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module