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Question

Answers

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

A) 1

B) 9

C) 8

D) 0

Answer
Verified

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 â€˜Bâ€™ is correct.

Note: The elaborate approach for the given equation is by substituting $\sec A$ with $\dfrac{1}{{\cos A}}$ and $\tan A$ with $\dfrac{{\sin A}}{{\cos A}}$ .

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 â€˜Bâ€™ is correct.

Note: The elaborate approach for the given equation is by substituting $\sec A$ with $\dfrac{1}{{\cos A}}$ and $\tan A$ with $\dfrac{{\sin A}}{{\cos A}}$ .

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