The value of sin (45° + A) — cos(45° — A)is:

Correct option is C

Given:
· We are asked to find the value of sin(45° + A) — cos(45° — A).
Concept Used:
· Use the standard trigonometric identities for sin and cos with angle addition and subtraction formulas.
· We know that:
· sin(45°) = cos(45°) = 1/√2.
Solution:
1. Expand the given expression: sin(45° + A) — cos(45° — A) = sin(45°)cos(A) + cos(45°)sin(A) — [cos(45°)cos(A) + sin(45°)sin(A)]
2. Substituting sin(45°) = cos(45°) = 1/√2: = (1/√2)cos(A) + (1/√2)sin(A) — [(1/√2)cos(A) + (1/√2)sin(A)]
3. Simplify the expression: = (1/√2)cos(A) + (1/√2)sin(A) — (1/√2)cos(A) — (1/√2)sin(A)
= 0
Thus, the value of the expression is 0.
Final Answer: (c) 0.