Here's the verification:
Using angle subtraction formula:
- cos(x - 5π/4) = cos(x)cos(5π/4) + sin(x)sin(5π/4)
Evaluating cosine and sine:
- cos(5π/4) = -√2/2
- sin(5π/4) = -√2/2
Substituting values:
- cos(x - 5π/4) = cos(x)(-√2/2) + sin(x)(-√2/2)
- cos(x - 5π/4) = -√2/2(cos x + sin x)
Therefore, the identity is verified:
cos(x - 5π/4) = -√2/2(cos x + sin x)
