Answer: The answer is [tex]\cos(x+y)=\cos x\cos y-\sin x\sin y.[/tex]
Step-by-step explanation: We are to find the sum or the difference that could be used to prove the following identity:
[tex]\cos(\pi+q)=-\cos q.[/tex]
To prove the above identity, the following sum which results in a difference, will be appropriate
[tex]\cos(x+y)=\cos x\cos y-\sin x\sin y.[/tex]
The proof is as follows
[tex]L.H.S.\\\\=\cos(\pi+q)\\\\=\cos \pi\cos q-\sin \pi\sin q\\\\=(-1)\cos q-0\times \sin q\\\\=-\cos q\\\\=R.H.S.[/tex]
Thus, the answer is [tex]\cos(x+y)=\cos x\cos y-\sin x\sin y.[/tex]
