Verified by Ajay Kumar
If \(\sec^2\theta+\tan^2\theta=\frac{7}{12}\), find the value of \(\sec^4\theta-\tan^4\theta\).
\(\frac{7}{12}\)
\(\frac{13}{12}\)
1
\(\frac{5}{12}\)
Answer: A
Solution: \(\sec^4\theta-\tan^4\theta=(\sec^2\theta-\tan^2\theta)(\sec^2\theta+\tan^2\theta)\). Since \(\sec^2\theta-\tan^2\theta=1\), the expression is \(1\times\frac{7}{12}=\frac{7}{12}\). Trick: Factor the difference of two squares. Source note: The printed condition \(\sec^2\theta+\tan^2\theta=\frac{7}{12}\) is not possible for a real angle, but the green-marked answer is retained.
यदि \(\sec^2\theta+\tan^2\theta=\frac{7}{12}\), तो \(\sec^4\theta-\tan^4\theta\) का मान ज्ञात कीजिए।
\(\frac{7}{12}\)
\(\frac{13}{12}\)
1
\(\frac{5}{12}\)
उत्तर: A
हल: \(\sec^4\theta-\tan^4\theta=(\sec^2\theta-\tan^2\theta)(\sec^2\theta+\tan^2\theta)\)। क्योंकि \(\sec^2\theta-\tan^2\theta=1\), इसलिए मान \(1\times\frac{7}{12}=\frac{7}{12}\) है। ट्रिक: दो वर्गों के अंतर का गुणनखंड करें। स्रोत संबंधी टिप्पणी: मुद्रित शर्त \(\sec^2\theta+\tan^2\theta=\frac{7}{12}\) किसी वास्तविक कोण के लिए संभव नहीं है, लेकिन हरे रंग से चिह्नित उत्तर को यथावत रखा गया है।
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