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

Question

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

Vedantu Content Team · Accepted Answer

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 $\dfrac{{\sin A}}{{\cos A}}$ .

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

NCERT Book Solutions

Reference Book Solutions

Question Papers

Exams

Quick Links

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

Book your FREE Online counselling session

Your FREE Online counselling session has been booked!

Please try again later

NCERT Book Solutions

Reference Book Solutions

Question Papers

Exams

Quick Links

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