if tan A = √2-1 then show that :tan A. √2----------

1.	if tan A = √2-1 then show that :tan A. √2---------- = ---------1+ tan²A. 4
Answer» Given,tan A = root(2) - 1 Then,tan A/ 1 + tan^2 A = root(2) - 1/ 1 + [root(2) - 1]^2 = root(2) - 1/ (1 + 2 +1 - 2root(2)) = (root(2) - 1) / (4 - 2root(2))= root(2)[1 - 1/root(2)]/ 4[1 - 2root(2)/4] = root(2)[1 - 1/root(2)]/ 4[1 - 1/root(2)] = root(2)/4 Hence proved

if tan A = √2-1 then show that :tan A. √2---------- = ---------1+ tan²A. 4

Answer»

Given,tan A = root(2) - 1

Then,tan A/ 1 + tan^2 A

= root(2) - 1/ 1 + [root(2) - 1]^2

= root(2) - 1/ (1 + 2 +1 - 2root(2))

= (root(2) - 1) / (4 - 2root(2))= root(2)[1 - 1/root(2)]/ 4[1 - 2root(2)/4]

= root(2)[1 - 1/root(2)]/ 4[1 - 1/root(2)]

= root(2)/4

Hence proved