Prove that: \( \sin (A+B+C+D)+\sin (A+B-C-D)+ \)
\[
\sin (A+B-C+D)+\sin (A+B+C-D)=4 \sin (A+B)
\...
Prove that: \( \sin (A+B+C+D)+\sin (A+B-C-D)+ \)
\[
\sin (A+B-C+D)+\sin (A+B+C-D)=4 \sin (A+B)
\]
\( \cos C \cos D \).
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