CBSE BoardEnglish MediumSTD 10MathsTrigonometric Identities1 Mark
MCQ
If $x=a \sec \theta$ and $y=b \tan \theta$, then $b^2 x^2-a^2 y^2=$
A
$ab$
B
$a^2-b^2$
C
$a^2+b^2$
✓
$a^2 b^2$
✓
Answer
Correct option: D.
$a^2 b^2$
Given, $\text{x}=\text{a}\sec\theta,\text{y}=\text{b}\tan\theta$
So,
$\text{b}^2\text{y}^2-\text{a}^2\text{y}^2$
$=\text{b}^2(\text{a}\sec\theta)^2-\text{a}^2(\text{b}\tan\theta)^2$
$=\text{b}^2\text{a}^2\sec^2\theta-\text{a}^2\text{b}^2\tan^2\theta$
$=\text{b}^2\text{a}^2(\sec^2\theta-\tan^2\theta)$
We know that,
$\sec^2\theta-\tan^2\theta=1$
$\text{b}^2\text{x}^2-\text{a}^2\text{y}^2=\text{a}^2\text{b}^2$
Hence, the correct option is $(D).$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.