Question

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

Answer 1

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)}`