Question

Please help verify the identity of cos (x+ -5pi/4) = -sqrt2/2 (cos x + sin x)

Answer 1

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)