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

tan A = 1

As we know

Now construct a right angle triangle right angled at B such that

∠ BAC = θ

Hence perpendicular = BC = 1 and base = AB = 1

By Pythagoras theorem,

AC² = AB² + BC²

⇒ AC² = (1)² + (1)²

⇒ AC² = 2

⇒ AC =

As,

⇒

Hence,

2 sin A cos A=

⇒ 2 sin A cos A=

⇒ 2 sin A cos A=1

= R.H.S

Hence proved.