Answer:
cos(x+5π/4) = (-√2/2)cos(x) + (√2/2)sin(x)
Step by step explanation:
We can use the trigonometric identity for cosine of the sum of two angles:
cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
Let a = x and b = 5π/4, then we have:
cos(x + 5π/4) = cos(x)cos(5π/4) - sin(x)sin(5π/4)
We can simplify this by using the values of cosine and sine of 5π/4:
cos(5π/4) = -√2/2 and sin(5π/4) = -√2/2
Substituting these values, we get:
cos(x + 5π/4) = cos(x)(-√2/2) - sin(x)(-√2/2)
Simplifying further:
cos(x + 5π/4) = (-√2/2)cos(x) + (√2/2)sin(x)
Therefore, we have rewritten cos(x+5π/4) in terms of sin x and cos x as:
cos(x+5π/4) = (-√2/2)cos(x) + (√2/2)sin(x)