I NEED HELP WITH TWO PROBLEMS! sin −θcos −5θ − cos −θsin −5θ AND cos −vcos 4v + sin −vsin 4v

Question

I need help for these problems to prepare for an upcoming test! ASAP

Answer 1

Recall that cos(-x) = cosx and sin(-x) = -sinx. That is, cosine is an even function and sine is an odd function.

So, sin(-θ)cos(-5θ) - cos(-θ)sin(-5θ) = cosθsin(5θ) - sinθcos(5θ) = sin(5θ - θ) = sin(4θ)

cos(-v)cos(4v) + sin(-v)sin(4v) = cosvcos(4v) - sinvsin(4v) = cos(v + 4v) = cos(5v)