Question

If $x=asec\theta$ and $y=btan\theta$ then $b^2{x}^2-a^2{y}^2=$

• A. $ab$
• B. $a^2-b^2$
• C. $a^2+b^2$
• D. $a^2{b}^2$

Answer 1

The correct option is D $a^2{b}^2$

$b^2{x}^2-a^2{y}^2$
$=b^2(asec\theta {)}^2-a^2(btan\theta {)}^2$
$=a^2{b}^2(se{c}^2\theta -ta{n}^2\theta )=a^2{b}^2(\because 1+ta{n}^2\theta =se{c}^2\theta )$