\(\sec^2 A - \tan^2 A\) का मान क्या है?
Understand the Problem
यह प्रश्न त्रिकोणमितीय सर्वसमिका (\sec^2 A - \tan^2 A = 1) का उपयोग करने के लिए कह रहा है। हमें (\sec^2 A - \tan^2 A) का मान ज्ञात करना है। त्रिकोणमितीय पहचान के अनुसार, (\sec^2 A - \tan^2 A) हमेशा 1 के बराबर होता है, चाहे A का मान कुछ भी हो।
Answer
(A) 1
Answer for screen readers
(A) 1
Steps to Solve
- Identify the trigonometric identity
The problem involves the trigonometric identity $ \sec^2 A - \tan^2 A $.
- Recall the trigonometric identity
The trigonometric identity states that $ \sec^2 A - \tan^2 A = 1 $ for any angle $A$ where $ \sec A $ and $ \tan A $ are defined.
- Apply the identity
Therefore, the value of $ \sec^2 A - \tan^2 A $ is 1.
(A) 1
More Information
The identity $ \sec^2 A - \tan^2 A = 1 $ is a direct consequence of the Pythagorean identity $ \sin^2 A + \cos^2 A = 1 $. Dividing the Pythagorean identity by $ \cos^2 A $, we get $ \tan^2 A + 1 = \sec^2 A $, which can be rearranged to $ \sec^2 A - \tan^2 A = 1 $.
Tips
A common mistake is to confuse this identity with other trigonometric identities. For example, some students might incorrectly recall the value of $ \sec^2 A - \tan^2 A $ as 0 or some other value. It's important to memorize and understand the fundamental trigonometric identities.
AI-generated content may contain errors. Please verify critical information
