Question

if tanx =x-1/4x, then secx - tanx is equal to​

Answer 1

Answer:

Step-by-step explanation:

option a) is the right one

Answer 2

Option a - $\sec x-\tan x=\frac{1}{2x},-2x$

Step-by-step explanation:

Given : If $\tan x=x-\frac{1}{4x}$

To find : The value of $\sec x-\tan x$ ?

Solution :

We know that,

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

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

$sec^2 x= 1+(x-\frac{1}{4x})^2$

$sec^2 x= 1+x^2+\frac{1}{16x^2}-\frac{1}{2}$

$sec^2 x= x^2+\frac{1}{16x^2}+\frac{1}{2}$

$sec^2 x= (x+\frac{1}{4x})^2$

$sec x= \pm(x+\frac{1}{4x})$

Now substitute the value $sec x= x+\frac{1}{4x}$,

$\sec x-\tan x=x+\frac{1}{4x}-(x-\frac{1}{4x})$

$\sec x-\tan x=x+\frac{1}{4x}-x+\frac{1}{4x}$

$\sec x-\tan x=\frac{2}{4x}$

$\sec x-\tan x=\frac{1}{2x}$

Now substitute the value $\sec x= -x-\frac{1}{4x}$,

$\sec x-\tan x=-x-\frac{1}{4x}-(x-\frac{1}{4x})$

$\sec x-\tan x=-x-\frac{1}{4x}-x+\frac{1}{4x}$

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

Therefore, Option a is correct.

#Learn more

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