1.

In a right triangle ABC right-angled at B. if `t a n A=1`, then verify that `2sinA cos A=1.`

Answer» `tanA=(BC)/(AB)`
`1=(BC)/(AB)`
`BC=AB`
`AC=sqrt(AB^2+BC^2)`
`=ABsqrt2`
`=sqrt3BC`
`SinA=(BC)/(AC)=(BC)/(sqrt2BC)=1/sqrt2
``CosA=(AB)/(AC)=(AB)/(sqrt2BC)=1/sqrt2`
`2CosASinA=2*1/sqrt2*1/sqrt2=1`


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