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

$\sin ^2 \frac{\pi }{8} + \sin ^2 \frac{3\pi }{8} + \sin ^2 \frac{5\pi }{8} + \sin ^2 \frac{7\pi }{8} = $

If $\sec \theta + \tan \theta = p, (p \neq 0)$,then $\sec \theta$ is equal to:

Evaluate: $\cos^2 76^\circ + \cos^2 16^\circ - \cos 76^\circ \cos 16^\circ$

If $\tan \theta + \sin \theta = m$ and $\tan \theta - \sin \theta = n,$ then

What is the simplified value of $\left[\frac{\left(\sec ^{3} x-\tan ^{3} x\right)}{(\sec x-\tan x)}\right]-2 \tan ^{2} x-\sec x \tan x ?$

Vedclass Test Series

Exam Paper Generator

Online Exam Module