Question

In a rigt triangle ABC right angled at B. If tan A=1,then verify that 2 sin A cos A =1.

Answer 1

Tan A=sinA/cosA=1

=>SinA=cosA

=>Angle A=45°(as SinA=cosA so base=perpendicular)

2sinAcosA=2*1/√2*1/√2

=1

Answer 2

$\huge\underline{ \underline{ \red{your \: \: answer}}}$$\sf\pink{tan \:A = 1 } \\ \sf\pink { = > \frac{sin \: A}{cos \: A} = tanA } \\ \sf\pink{ = > \frac{sin \: A}{cos \: A} = 1 } \\ \sf\pink{ = > sin \: A = cos \: A} \\ \sf\pink{ = > sin \: 45° = cos \: 45°} \\ \sf\pink{ = > a = 45°} \: ( \sin\alpha = \cos \alpha \: when \: \alpha = 45°)$$\sf\pink{2sin \: A \: cos \: A } \\ \sf\pink{ = > 2sin45°cos45°} \\ \sf\pink{ = > 2 \times \frac{1}{ \sqrt{2} } \times \frac{1}{ \sqrt{2} } } \\ \sf\pink{ = > \frac{2}{ \sqrt{2} \times \sqrt{2} } } \\ \sf\pink{ = > \frac{2}{ \sqrt{4} } } \\ \sf\pink{ = > \frac{2}{2} } \\ \sf\pink{ = > 1} \\ \sf\pink{LHS = RHS}$

$\large\boxed{ \fcolorbox{red}{yellow}{hope it help you}}$