Q. 26 B4.1( 19 Votes )

# 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.

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