Verified by Ajay Kumar
Simplify the expression: \((\sin\theta+\operatorname{cosec}\theta)^2+(\cos\theta+\sec\theta)^2-(\tan\theta+\cot\theta)^2\).
5
0
1
\(\frac12\)
Answer: A
Solution: Expand the first two squares and use \(\sin^2\theta+\cos^2\theta=1\), \(\operatorname{cosec}^2\theta=1+\cot^2\theta\), and \(\sec^2\theta=1+\tan^2\theta\). After subtracting \((\tan\theta+\cot\theta)^2\), the terms cancel, leaving 5. Trick: Use the Pythagorean identities before combining the terms.
व्यंजक को सरल कीजिए: \((\sin\theta+\operatorname{cosec}\theta)^2+(\cos\theta+\sec\theta)^2-(\tan\theta+\cot\theta)^2\)।
5
0
1
\(\frac12\)
उत्तर: A
हल: पहले दो वर्गों को खोलें और \(\sin^2\theta+\cos^2\theta=1\), \(\operatorname{cosec}^2\theta=1+\cot^2\theta\) तथा \(\sec^2\theta=1+\tan^2\theta\) का प्रयोग करें। \((\tan\theta+\cot\theta)^2\) घटाने के बाद संबंधित पद कट जाते हैं और 5 बचता है। ट्रिक: पदों को जोड़ने या घटाने से पहले पाइथागोरस सर्वसमिकाओं का प्रयोग करें।
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