Question

If $\sec x-\tan x=0.5,$ then select the correct statement(s).

• A. $\sec x=2.5$
• B. $\sec x=1.25$
• C. $\tan x=2$
• D. $\tan x=0.75$

Answer 1

Answer: (B), (D)

$\tan x=0.75$

Given: $\sec x-\tan x=0.5...\left(A\right)$
To find: $\sec x$
Using the reciprocal identity, i.e.
$\sec x-\tan x=\frac{1}{\sec x+\tan x}$

$\Rightarrow \sec x+\tan x=\frac{1}{\sec x-\tan x}=\frac{1}{0.5}=2$

$\Rightarrow \sec x+\tan x=2...\left(B\right)$

Now, adding both the expressions $A\&B,$ we get:

$2\sec x=0.5+2\Rightarrow 2\sec x=2.5$

$\Rightarrow \sec x=\frac{2.5}{2}=1.25$

Now, substituting $\sec x$ in $A,$ we get:

$1.25-\tan x=0.5$
$\Rightarrow \tan x=1.25-0.5=0.75$