Question

if secx +tanx=p then what is the value of secx-tanx

Answer 1

sec^2x-tan^2x = 1
(sec x+ tan x)(sec x-tan x) =1
p(sec x-tan x) =1
sec x- tan x =1/p

Answer 2

We have:

$\sec x$ + $\tan x$ = p                 ..............(1)

We have to find, the value of $\sec x$ - $\tan x$=?  

Solution:

Using the trigonometric identity:

$\sec^2 x-\tan^2 x$ = 1

⇒ ($\sec x$ + $\tan x$)($\sec x$ - $\tan x$) = 1 [ ∵ $a^{2} -b^{2}$ = (a + b)(a - b)]

From equation (1), we get

(p)($\sec x$ - $\tan x$) = 1

Dividing both sides by 2, we get

$\sec x$ - $\tan x$ = $\dfrac{1}{p}$

∴ $\sec x$ - $\tan x$ = $\dfrac{1}{p}$

Thus, if $\sec x$ + $\tan x$ = p, then the value of "$\sec x$ - $\tan x$ =  $\dfrac{1}{p}$".