Question: Use trigonometric and hyperbolic identities to solve trigonometric equations and to simplify trigonometric expressions

Simplify

1. \[\cos 7\omega t\,\cos 3\omega t+\sin 7\omega t\,\sin 3\omega t\]
2. \[\sin 2\omega t\,\,\cos (2\omega t-k)-\cos 2\omega t\,\,\sin (2\omega t-k)\]
   (c) \[-1+{{\cosh }^{2}}A\] (use the exponential representation)
   (d) \[\frac{1+\,\sinh \,2A\,+\,\cosh \,2A}{1-\,\sinh \,2A\,-\,\cosh \,2A\,}\]
   
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