sinh2t*cosat is equal to? use trigonometric formula

The expression you provided involves hyperbolic and trigonometric functions. However, there isn't a direct trigonometric formula to simplify "sinh2t*cosat".

The hyperbolic sine function, sinh(x), can be expressed in terms of exponential functions as follows:

sinh(x) = (e^x - e^-x) / 2

So, sinh(2t) = (e^(2t) - e^(-2t)) / 2

The cosine function, cos(x), is a standard trigonometric function.

Therefore, the expression sinh2t*cosat becomes:

= [(e^(2t) - e^(-2t)) / 2] * cos(at)

This is the most simplified form using standard trigonometric and hyperbolic identities. If you have specific identities or formulas you'd like to use, please provide them.