Question

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

• A. $\pm \sqrt{2}$
• B. $\pm \sqrt{3}$
• C. $\pm 2$
• D. $\pm 1$

Answer 1

The correct option is D $\pm 1$

${(\tan x+\sec x)}^2{(\tan y+\sec y)}^2{(\tan z+\sec z)}^2$
$=({\sec }^{2}x-{\tan }^{2}x)({\sec }^{2}y-{\tan }^{2}y)({\sec }^{2}z-{\tan }^{2}z)$
$=1\times 1\times 1=1=k^2$
$\therefore K=\pm 1$