Question

If tan A=root 2 - 1, then show that sin A cos A=root 2/ 4

Answer 1

Tan A = √2 - 1

Tan A = p / b { p: perpendicular , b:base}

h : hypotenuse

(√ 2 - 1 ) / 1 = p / b

p= √2 - 1 , b = 1

By pythagoras theorem ,

p² + b² = h²

(√2 - 1 )² + (1)² = h²

2 + 1 - 2√2 + 1 = h ²

h² = [4 - 2√2 ]

Sin A = p / h , Cos A = b / h

Sin 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 / 4
Hence Proved

Answer 2

Answer:

root2/4

Step-by-step explanation:

hope it helps you buddy ✌️✌️