Question

If tan A=√2-1, then cos A sin A _________
please solve with steps....

Answer 1

Given,
tan A=√2-1
∴ then cos A sin A = √2 / 4.

How,
= opp*adj/hyp^2 
= (√2-1)*1/2(2-√2) 
= (√2-1)(2+√2)/2(2-√2)(2+√2) 
= (2√2+2-2-√2)/2(4-2) 
= √2 / 4

Answer 2

Step-by-step explanation:

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

$\leqslant$