If tan theta + sec theta = e^x,then cos theta | vedclass

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

Question

(B) We are given that $	an 	heta + \sec 	heta = e^x$  --- $(i)$We know the trigonometric identity $\sec^2 	heta - 	an^2 	heta = 1$.This can be f

Vedclass · Accepted Answer

$\frac{2}{e^x + e^{-x}}$

Vedclass · Answer

(B) We are given that $	an 	heta + \sec 	heta = e^x$  --- $(i)$We know the trigonometric identity $\sec^2 	heta - 	an^2 	heta = 1$.This can be factored as $(\sec 	heta - 	an 	heta)(\sec 	heta + 	an 	heta) = 1$.Substituting the value from $(i)$,we get $(\sec 	heta - 	an 	heta) e^x = 1$,which implies $\sec 	heta - 	an 	heta = e^{-x}$ --- $(ii)$Adding equations $(i)$ and $(ii)$:$(	an 	heta + \sec 	heta) + (\sec 	heta - 	an 	heta) = e^x + e^{-x}$$2 \sec 	heta = e^x + e^{-x}$Since $\cos 	heta = \frac{1}{\sec 	heta}$,we have $\sec 	heta = \frac{e^x + e^{-x}}{2}$.Therefore,$\cos 	heta = \frac{2}{e^x + e^{-x}}$.

If $\tan \theta + \sec \theta = e^x$,then $\cos \theta$ equals

Similar Questions

If $a \sin^2 x + b \cos^2 x = c$,$b \sin^2 y + a \cos^2 y = d$ and $a \tan x = b \tan y$,then $\frac{a^2}{b^2}$ is equal to

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

The value of $\frac{(\tan 69^{\circ} + \tan 66^{\circ})}{(1 - \tan 69^{\circ} \tan 66^{\circ})}$ is

Let $A_0 A_1 A_2 A_3 A_4 A_5$ be a regular hexagon inscribed in a circle of unit radius. Then the product of the lengths of the line segments $A_0 A_1$,$A_0 A_2$,and $A_0 A_4$ is

If $A + B + C = 180^\circ,$ then $\frac{\sin 2A + \sin 2B + \sin 2C}{\cos A + \cos B + \cos C - 1} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module