Verified by Ajay Kumar
Simplify: \((\sin A+\operatorname{cosec} A)^2+(\cos A+\sec A)^2-(\tan^2 A+\cot^2 A)\).
0
7
1
5
Answer: B
Solution: Expand the squares and use \(\sin^2 A+\cos^2 A=1\), \(\sec^2 A-\tan^2 A=1\), and \(\operatorname{cosec}^2 A-\cot^2 A=1\). The expression simplifies to \(1+4+1+1=7\). Trick: Pair cosec² with cot² and sec² with tan² to use the standard identities.
सरल कीजिए: \((\sin A+\operatorname{cosec} A)^2+(\cos A+\sec A)^2-(\tan^2 A+\cot^2 A)\)।
0
7
1
5
उत्तर: B
हल: वर्गों को खोलें और \(\sin^2 A+\cos^2 A=1\), \(\sec^2 A-\tan^2 A=1\) तथा \(\operatorname{cosec}^2 A-\cot^2 A=1\) का प्रयोग करें। व्यंजक सरल होकर \(1+4+1+1=7\) हो जाता है। ट्रिक: cosec² को cot² के साथ और sec² को tan² के साथ रखकर मानक सर्वसमिकाओं का प्रयोग करें।
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