Question

if sin x + cos x = 1 then find sin 2x

Answer 1

by squaring
sin x + cos x=1
sin square x + cos square x + 2cos x sin x = 2sin x cos x.
(sin2 x + cos 2 =1)
2 cos x sin x =0
and
sin 2x = 2 cos x sin x
so
sin 2x = 0.

Answer 2

sin x + cos x=1
by squaring on both sides, we get

=>sin ^2+ cos ^2 = 1^2
{(a^2+ b^2=a^2+b^2+2ab)}
=>(sin x +cos x)^2=1
=>sin^2+cos ^2+2sin. cos =1
=>1+2sin x.cosx=1 {(Sin ^2+cos ^2 =1)}
=>2sin x.cosx =1-1
=>2sinx. 1/sin {cos =1/ sin }
=>2x proved.

hope this helps u....