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.

Answer :

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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