Question:
Simplify the expression: \(\dfrac{1 – \cos^2 x}{1 – \sin^2 x}\)
व्यंजक को सरल कीजिए: \(\dfrac{1 – \cos^2 x}{1 – \sin^2 x}\)
Options:
- \(\tan^2 x\)
- 1
- \(\sec^2 x\)
- \(1 – \tan^2 x\)
- \(\tan^2 x\)
- 1
- \(\sec^2 x\)
- \(1 – \tan^2 x\)
Correct Answer: a)
Explanation:
Using trigonometric identities: \(1 – \cos^2 x = \sin^2 x\) and \(1 – \sin^2 x = \cos^2 x\).
Thus, \(\dfrac{\sin^2 x}{\cos^2 x} = \tan^2 x\).
त्रिकोणमितीय सर्वसमिकाओं का उपयोग करने पर: \(1 – \cos^2 x = \sin^2 x\) और \(1 – \sin^2 x = \cos^2 x\)।
अतः \(\dfrac{\sin^2 x}{\cos^2 x} = \tan^2 x\)।