Verified by Ajay Kumar
In a right triangle ABC, right-angled at B, if \(\tan A=1\), what is the value of \(2\sin A\cos A\)?
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Answer: D
Given \(\tan A=1\), so \(A=45^\circ\) because A is an acute angle in a right triangle. Thus, \(\sin A=\frac1{\sqrt2}\) and \(\cos A=\frac1{\sqrt2}\). Therefore, \(2\sin A\cos A=2\times\frac1{\sqrt2}\times\frac1{\sqrt2}=1\). Trick: Use \(2\sin A\cos A=\sin2A=\sin90^\circ=1\).
एक समकोण त्रिभुज ABC में, जिसका कोण B समकोण है, यदि \(\tan A=1\) है, तो \(2\sin A\cos A\) का मान क्या है?
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उत्तर: D
दिया है \(\tan A=1\), इसलिए \(A=45^\circ\), क्योंकि समकोण त्रिभुज में A न्यून कोण है। अतः \(\sin A=\frac1{\sqrt2}\) और \(\cos A=\frac1{\sqrt2}\)। इसलिए \(2\sin A\cos A=2\times\frac1{\sqrt2}\times\frac1{\sqrt2}=1\)। ट्रिक: \(2\sin A\cos A=\sin2A=\sin90^\circ=1\) का प्रयोग करें।
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