Answer :

Consider ΔABC to be a right - angled triangle.



tanA = 1 = BC/AB


BC = AB


Also, tanA = 1 = sinA/cosA


sinA = cosA


By Pythagoras theorem, (hypotenuse)2 = (perpendicular)2 + (base)2


AC2 = BC2 + AB2


= AC2 = 2BC2


= (AC/BC)2 = 2


= AC/BC = √2


cosecA = √2


sinA = 1/√2 = cosA


2 sinA cosA = 2(1/√2)( 1/√2)


= 2(1/2)


= 1


LHS = RHS


HENCE PROVED


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