Question

If tan A =√2-1, then prove that sin A cos A =1/2√2

Answer 1

sin/cosA=
$\sqrt{2 - \: \: 1}$
sinA/cosA+1=√2

sinA+cosA/cosA=√2

sinA×cosA+(cosA )(cosA)/cos^A=√2
sinA×cosA+cos^A/cos^A=√2
cosA(sinA+cosA)/cos^A=√2
sinA+cosA/cosA=√2
sinA×cosA=1/2√2