If sin⁡θ+cos⁡θ=√2, then what is the value of 8sin⁡θcos⁡θ ?

Correct option is D

 Given:

sin⁡θ+cos⁡θ= $$\sqrt 2$$​​

Formula Used:
$$sin^2 x + cos^2 x$$​ = 1
Solution:
sin⁡θ+cos⁡θ=√2
By, squaring both sides of the above equation we get,
=>$$[sin⁡θ+cos⁡θ]^2=[{\sqrt2}]^2$$​
=> $$sin^2 θ + cos^2 θ + 2sin θ.cos θ = 2$$​​
As we know that, $$sin^2 x + cos^2 x$$​= 1
=> 1 + 2sin θcos θ = 2
=> 2sin θcos θ = 2-1 = 1

Multiply by 4 both sides,

∴ 8sin θcos θ = 1$$\times 4 = 4$$​