Question

If $\sec A+\tan A=m$ and $\sec A-\tan A=n$, find the value of $\sqrt{mn}$.

• A. $0$
• B. $\pm 1$
• C. $\pm 2$
• D. $\pm 3$

Answer 1

The correct option is B $\pm 1$

Use trigonometry formula:

$se{c}^2\theta -ta{n}^2\theta =1$

$secA+tanA=m$ ......(1)

$secA-tanA=n$ .........(2)

multiply the equations (1) and (2),

$(secA+tanA)(secA-tanA)=mn$

$se{c}^{2}A-ta{n}^{2}A=mn$

$1=mn$

Therefore, $\sqrt{mn}=\pm 1$