Question

Choose the correct option. Justify your answer
$9{\sec ^2}A - 9{\tan ^2}A = $
A) 1
B) 9
C) 8
D) 0

Answer 1

Hint: Here, we will solve the given trigonometric equation by the use of the trigonometric identity ${\sec ^2}A - {\tan ^2}A = 1$ and trigonometric formulae.
Given,
$9{\sec ^2}A - 9{\tan ^2}A \to (1)$
Let us common $9$ from equation (1), we get
$ \Rightarrow 9({\sec ^2}A - {\tan ^2}A) \to (2)$
Since, we know the trigonometric identity i.e.., ${\sec ^2}A - {\tan ^2}A = 1$. Therefore, equation (2) can be written as
$ \Rightarrow 9(1) = 9$
Hence, the value of $9{\sec ^2}A - 9{\tan ^2}A$ is $9$.
Therefore, from the given options ‘B’ is correct.
Note: The elaborate approach for the given equation is by substituting $\sec A$ with $\dfrac{1}{{\cos A}}$ and $\tan A$ with $\dfrac{{\sin A}}{{\cos A}}$ .