Engineering How were tangent terms derived in solving for eqn (2) in a second-order circuit?

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The discussion centers on the derivation of tangent terms in the solution of a second-order circuit equation. The author expressed confusion about the transition to tangent terms in the final steps of the solution. It was clarified that the solver set equation (2) to zero and factored out the common term 5(cos 21.749t). This step is crucial for simplifying the equation and deriving the tangent terms. Understanding this process is essential for grasping the overall solution to the circuit problem.
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Homework Statement
Find the expression for ##v(t)##
Relevant Equations
SEE ATTACHED PHOTO
I was trying to follow the solution for this problem and got stuck in the last portion of the solution. I encircled the part that I did not understand. I can't figure out how the solver was able to come up with tangent terms. Please enlighten me. TIA
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The author equated eqn (2) to 0
then extracted (and divided both sides by) the common factor 5(cos 21.749t)
 

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