Which of the following options is a Pythagorean Identity sin

Which of the following options is a Pythagorean Identity? (sin(x) + cos(x))2 sin^2(x) - cos^2(x) = 1 sin(x) + cos(x))^2= 1 + 2sin(x) cos(x) (sin(x) + cos(x))^2 = 1 - 2sin(x)cos(x)

Solution

(sin(x)+cos(x))²=sin²(x)+cos²(x) +2sin(x)cos(x)

sinx =oppositeside/hypotenuse , cosx=adjacentside/hypotenuse

sin²x+cos²x=(oppositeside²/hypotenuse²)+(adjacentside²/hypotenuse²)

sin²x+cos²x=(oppositeside²+adjacentside²)/hypotenuse²

we know by pythogorus theorem oppositeside²+adjacentside²=hypotenuse²

sin²x+cos²x=hypotenuse²/hypotenuse²

sin²x+cos²x=1

so (sin(x)+cos(x))²=1 +2sin(x)cos(x)