Question

\(7 \sec^2 A - 7 \tan^2 A =\)

• A. 49
• B. 7
• C. 14
• D. 0

Hint:

Memorize the three Pythagorean identities: \(\sin^2 \theta + \cos^2 \theta = 1\), \(1 + \tan^2 \theta = \sec^2 \theta\), and \(1 + \cot^2 \theta = \csc^2 \theta\). They are essential for simplifying trigonometric expressions.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This question uses one of the fundamental Pythagorean identities in trigonometry.

Step 2: Key Formula or Approach:
The relevant trigonometric identity is:
\[ \sec^2 A - \tan^2 A = 1 \]

Step 3: Detailed Explanation:
The given expression is \(7 \sec^2 A - 7 \tan^2 A\).
We can see that 7 is a common factor in both terms. Let's factor it out:
\[ 7 (\sec^2 A - \tan^2 A) \] Now, we substitute the value of the identity \(\sec^2 A - \tan^2 A = 1\) into the expression:
\[ = 7 (1) \] \[ = 7 \]

Step 4: Final Answer:
The value of the expression is 7. This corresponds to option (B).