Question

sec x - tan x =√3 prove it

Answer 1

Answer:

Step-by-step explanation:

by the way it is solve the equation

Answer 2

ANSWER:  

The value of x in sec x - tan x =√3 is $30^{\circ}$

SOLUTION:

Given that, we have to solve $\sec x-\tan x=\sqrt[2]{3}$  ---- (1)

Now, we know that, $\sec \theta^{2}-\tan \theta^{2}=1$

$\begin{array}{c}{(\sec \theta-\tan \theta)(\sec \theta+\tan \theta)=1} \\\\{\sec \theta+\tan \theta=\frac{1}{\sec \theta-\tan \theta}}\end{array}$

$\sec x+\tan x=\frac{1}{\sqrt{3}}$  --- (2) [by using equation (1)]

Now, add (1) and (2), we get

$\begin{array}{l}{2 \sec x+0=\sqrt{3}+\frac{1}{\sqrt{3}}} \\\\ {2 \sec x=\frac{3+1}{\sqrt{3}}} \\\\ {2 \sec x=\frac{4}{\sqrt{3}}} \\\\ {\sec x=\frac{2}{\sqrt{3}}} \\\\ {\frac{1}{\cos x}=\frac{2}{\sqrt{3}}} \\\\ {\cos x=\frac{\sqrt{3}}{2}} \\\\ {\cos x=\cos 30}\end{array}$

Hence the value of x in sec x - tan x =√3 is $30^{\circ}$