Question

If (tan x +sec x)(tan y + sec y)(tanz +sec z) = (sec x - tan x )(sec y - tan y ) (secz - tan z) = K, then the value of K is

• A.
  
• B.
  
• C. ±2
• D. ±1

Answer 1

The correct option is D

±1

Divide and multiply
(tan x + sec x) (tan y + sec y)(tan z + sec z) to (sec x - tan x ) (sec y - tan y ) (sec z - tan z)

$\frac{(secx-tanx)(secy-tany)(secz-tanz)\times \left[\right(tanx+secx\left)\right(tany+secy\left)\right(tanz+secz\left)\right]}{(tanx+secx)(tany+secy)(tanz+secz)}$

$=\frac{1}{(tanx+secx)(tany+secy)(tanz+secz)}$

Suppose (tan x +sec x) (tan y +sec y) (tan z + sec z) =a

Then middle term becomes $\frac{1}{a}$
$a=\frac{1}{a}$
$a^2=1a=\pm 1$
So, $k=a=\pm 1$