Question

if sin x+cos x=1,then find the value of sin x.cos x

Answer 1

sinx + cosx = 1 
take square both sides, 
sin²x + cos²x + 2sinx.cosx = 1 

we know, 
sin²x + cos²x = (1)²
1 + 2sinx.cosx = 1 
1 -1 = 2.sinx.cosx
sins.cosx = 0/2 = 0
sinx.cosx = 0 

Answer 2

Sin.x+cos.x=1

Squaring both sides

(Sin.x+cos.x)^2=1^2

Sin.x^2+cos.x^2+2sin.xcos.x=1

1+2sin.xcos.x=1

2sin.xcos.x=1-1

Sin.xcos.x=0÷2

Sin.xcos.x=0