If tan A = root2-1, then show that sinA. CosA=root2/4

1.	If tan A = root2-1, then show that sinA. CosA=root2/4
Answer» Tan A = √2 - 1Tan A = p / b { p: perpendicular , b:base}h : hypotenuse(√ 2 - 1 ) / 1 = p / bp= √2 - 1 , b = 1By pythagoras theorem ,p² + b² = h²(√2 - 1 )² + (1)² = h²2 + 1 - 2√2 + 1 = h ²h² = [4 - 2√2 ]Sin A = p / h , Cos A = b / hSin A Cos A = ( p * b ) / h²=> (√ 2 - 1 ) / ( 4 - 2 √2)Rationalize Denomonator ,=> ( √ 2 - 1 ) * ( 4 + 2 √2 ) / ( 4 - 2 √2 )(4 + 2 √2)=> (4 √2 + 4 - 4 - 2√2 ) / ( 16 - 8 )=> 2 √2 / 8=> √2 / 4Hence Proved

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