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

$9$

Determine the correct option.

The explanation for the correct option:

We know that, ${\sec }^{2}A-{\tan }^{2}A=1$.

Factor out $9$ in the given equation and use the above identity:

$\begin{array}{rcl}9{\sec }^{2}A-9{\tan }^{2}A& =& 9\left({\sec }^{2}A-{\tan }^{2}A\right)\\ & =& 9\left(1\right)\left[\because {\sec }^{2}A-{\tan }^{2}A=1\right]\\ & =& 9\end{array}$

Therefore, $9{\sec }^{2}A-9{\tan }^{2}A=9$.

We know that, ${\sec }^{2}A-{\tan }^{2}A=1$.

Factor out $9$ in the given equation and use the above identity:

$\begin{array}{rcl}9{\sec }^{2}A-9{\tan }^{2}A& =& 9\left({\sec }^{2}A-{\tan }^{2}A\right)\\ & =& 9\left(1\right)\left[\because {\sec }^{2}A-{\tan }^{2}A=1\right]\\ & =& 9\end{array}$

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

Hence, the correct option is (B) i.e, $9$.

The explanation for the incorrect option:

since the value determined $9{\sec }^{2}A-9{\tan }^{2}A=9$ is not equal to the value mentioned in Option A, Option C, and Option D.

Option A, Option C, and Option D are an incorrect options.

Hence, the correct option is (B) i.e, $9$.