Question

(sin(A) + cos(A))² + (sin(A)-cos(A))² = 2

Answer 1

We can expand and simplify both sides of the equation using trigonometric identities. Let's proceed with the verification:

• Starting with the left-hand side (LHS):

(sin(A) + cos(A))² + (sin(A) - cos(A))²

• Expanding each squared term:

(sin(A) + cos(A))(sin(A) + cos(A)) + (sin(A) - cos(A))(sin(A) - cos(A))

• Using the FOIL method (First, Outer, Inner, Last):

sin²(A) + 2sin(A)cos(A) + cos²(A) + sin²(A) - 2sin(A)cos(A) + cos²(A)

• Combining like terms:

2sin²(A) + 2cos²(A)

• Using the identity sin²(A) + cos²(A) = 1:

2(1) = 2

Right-hand side Hence verified