If tan A=√2 – 1 then prove that .

Proof:

We know,

So, Let perpendicular = (√2 – 1)k

Base = k

Then, By pythagoras theorem

Hypotenuse² = Perpendicular² + Base²

⇒ Hypotenuse² = ((√2 – 1)k)² + k²

⇒ Hypotenuse² = (2 + 1 – 2√2)k² + k²

⇒ Hypotenuse² = (4 – 2√2)k²

Also,

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