If tan A = √2 – 1, show that tan A/1+tan^2 A = root2/4
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Heya User,
Hope you find your solution
Hope you find your solution
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Solution:
Given tanA= √2-1-----(1)
i) 1+ tan²A
= 1+(√2-1)²
= 1+(√2)²+1²-2*√2*1
/* (a-b)² = a²-2ab+b² * /
= = 1+2+1-2√2
= 4-2√2
= 2*2-2√2
= 2*√2*√2-2√2
Take 2√2 common, we get
= 2√2(√2-1) ----(2)
Now ,
LHS=
=
/* from (1) and (2) */
after cancellation, we get
=
/* Rationalising the denominator, we get
=
=
= $\frac{\sqrt{2}}{4}$
= RHS
Therefore,
= $\frac{\sqrt{2}}{4}$
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