How do I simplify number 14? Prove Identities or Simplify using sum and difference formula.

Question

asked Jan 6, 2023 230k views

1 Answer

Jenner La Fave · Answer 1 · 2023-01-10T14:58:08+0000

In this case, we will use the sum formula for the cosine to write an equivalent expression. Given angles a and b we have that

$\cos (a+b)=\cos (a)\cos (b)\text{ - sin(a)sin(b)}$

In our case , we have that a=pi, b=x. So

$\cos (\pi+x)=\cos (\pi)\cos (x)\text{ -sin(pi)sin(x)}$

Recall that

$\cos (\pi)=\text{ -1}$

and

$\sin (\pi)=0$

so we have that

$\cos (\pi+x)=\text{ -1}\cdot\cos (x)\text{ - 0}\cdot\sin (x)=\text{ -cos(x)}$