Question

Choose the correct option. Justify your choice.
$9{\sec }^{2}A-9{\tan }^{2}A=$?

• A. $1$
• B. $9$
• C. $8$
• D. $0$

Answer 1

The correct option is B $9$

now, $9{\sec }^{2}A-9{\tan }^{2}A$

$=9({\sec }^{2}A-{\tan }^{2}A)$

$=9(\frac{1}{{\cos }^{2}A}-\frac{{\sin }^{2}A}{{\cos }^{2}A})$

$(\sec \theta =\frac{1}{\cos \theta }\tan \theta =\frac{\sin \theta }{\cos \theta })$

$=9\left(\frac{1-{\sin }^{2}A}{{\cos }^{2}A}\right)$

$=9\frac{{\cos }^{2}A}{{\cos }^{2}A}({\sin }^2\theta +{\cos }^2\theta =1)$

$=9$