Question

if sinA+cosA=√2 then the value of sinA.cosA=​

Answer 1

Answer:

we know that,

(a+b)^2= a^2+b^2+2ab

similarly,

=> (sinA+cosA)^2=( sinA )^2+(cosA)^2

+2sinAcosA

=> (√2)^2=1+2sinAcisA

{. (sinA)^2+(cosA)^2=1}

=> 2=1+2sinAcosA

=> 1=2sinAcosA

=> 1/2=sinAcosA

thus ,the value of sinAcosA=1/2

I hope it would help you

thank you

Answer 2

(SinA+cosA)^2= 2
Sin^2x+cos^2x+ 2sinx.cosx=2
1+2sin x cos x =2
Sin x.cos x = 1/2